np_exp_()_np_log_().ipynb

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      "authorship_tag": "ABX9TyOoBBe+uTAo+oVf5VUR4jkU",
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      "cell_type": "markdown",
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    {
      "cell_type": "markdown",
      "source": [
        "NumPyのexp関数で指数関数を計算する3つの方法まとめ\n",
        "\n",
        "https://www.headboost.jp/numpy-exp/"
      ],
      "metadata": {
        "id": "87m7xC69A5I5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np"
      ],
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      },
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      "outputs": []
    },
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      "source": [
        "np"
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      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<module 'numpy' from '/usr/local/lib/python3.8/dist-packages/numpy/__init__.py'>"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.arange(0, 5, 0.5)"
      ],
      "metadata": {
        "id": "rmmhYlBfBLM7"
      },
      "execution_count": 3,
      "outputs": []
    },
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        "x"
      ],
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      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp(x)"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/"
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        "outputId": "e54a31c5-468c-4c74-e107-2cca992bac7d"
      },
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      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.        ,  1.64872127,  2.71828183,  4.48168907,  7.3890561 ,\n",
              "       12.18249396, 20.08553692, 33.11545196, 54.59815003, 90.0171313 ])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp(0.5)"
      ],
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        },
        "id": "ftG2Jh_3BTbm",
        "outputId": "ff1c6765-035e-4cb8-8fb1-2a1d760ae30b"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.6487212707001282"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp(1)"
      ],
      "metadata": {
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        },
        "id": "GzsheTz9BcrA",
        "outputId": "0d1dc116-4dbf-4cfb-eb7f-66436e6e6633"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.718281828459045"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp(2)"
      ],
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        "outputId": "c8005f4b-d696-4bf5-e872-8b598a36c238"
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      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7.38905609893065"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp(3)"
      ],
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        "id": "1laJBWaOBksm",
        "outputId": "64ec1b2f-1f54-489f-b88b-525203fcd26e"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20.085536923187668"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp(x)"
      ],
      "metadata": {
        "colab": {
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        },
        "id": "JXD5chm3Bl2C",
        "outputId": "31ffdf81-185a-479a-b94c-7b08bfa97947"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.        ,  1.64872127,  2.71828183,  4.48168907,  7.3890561 ,\n",
              "       12.18249396, 20.08553692, 33.11545196, 54.59815003, 90.0171313 ])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.expm1(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F7T0xxH-Bogg",
        "outputId": "66bebafb-37f3-495f-ed9b-dc8609434cfa"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.        ,  0.64872127,  1.71828183,  3.48168907,  6.3890561 ,\n",
              "       11.18249396, 19.08553692, 32.11545196, 53.59815003, 89.0171313 ])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.exp2(x)"
      ],
      "metadata": {
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        },
        "id": "wA8KrywOBrMY",
        "outputId": "d9598555-9f26-417c-ec20-39bd56302d54"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1.        ,  1.41421356,  2.        ,  2.82842712,  4.        ,\n",
              "        5.65685425,  8.        , 11.3137085 , 16.        , 22.627417  ])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "eO_wpb8IBtyI"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "Y0rMfmYCCEhq"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt"
      ],
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        "id": "q6kFEH3uCIwU",
        "outputId": "be1d9695-a392-4d39-bd72-bc352eccb8ac"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<module 'matplotlib.pyplot' from '/usr/local/lib/python3.8/dist-packages/matplotlib/pyplot.py'>"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.exp(x), label=\"exp\")\n",
        "plt.plot(np.expm1(x), label=\"expm1\")\n",
        "plt.plot(np.exp2(x), label=\"exp2\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "6nkjNlQACJXh",
        "outputId": "a82dc0ef-37f2-439c-a085-3d01af121069"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.exp(x), label=\"exp\")\n",
        "plt.plot(np.exp(x)-1, label=\"exp-1\")\n",
        "plt.plot(np.exp2(x), label=\"exp2\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "VD4XMitwCXoL",
        "outputId": "fde28414-9f0f-4b13-a755-610ce86dd643"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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a+BTEngkX/6fRkYJKClwIMSRsPtTAXz44wjtpz2HtbIHrXobIaKNjBZUUuBAi7DV2OPnRS/v4YeIWJrVt8Y+8M6YbHSvoZA5cCBHWtNbct2Y/I+yl3On+G5x+QdifrLi/ZAQuhAhrz31UzpbiSraOeAaTLw6ufgpMw2NsKgUuhAhbh+raeeztIv6U+gYp7Ydgyeohc7KG/hgef00JIYYch9u/ZPCiyHwubn8F5iyDCZcYHWtQyQhcCBGWHn+nmIbaSl5PfBriJ8NX/8PoSINOClwIEXY2Ftfz962lrEt7FmtnO1z3BliijI416KTAhRBhpaHdyU/W7OO+pH9zZtuHcOlvIX2K0bEMIQUuhAgbPp/mxy/tI8NxhNv1Shh/Mcz5rtGxDCMFLoQIG3/fWsZHh6rYNuJpTDoBrvozKGV0LMNIgQshwkJRTRuPv1PMk2mvktj2Mdz4MsSmGh3LULKMUAgR8nqWDC627WNR2+sw7wdwxoVGxzKcFLgQIuT96u0iWuqP8hvzU5A+DS58xOhIIUGmUIQQIW19YR3PfVTKe2nPYulywHXLwWw1OlZIkAIXQoSsujYH963Zx0+TNnJ62zZY/HtIm2h0rJAhBS6ECEk+n+ZH/9xHtruEW3kWJiyGnO8YHSukSIELIULS8i1H2FlSxbaUZ1AqBa78n2G9ZPBEpMCFECHnQFUrv117kOVpLxPfVgY3vQYxKUbHCjmyCkUIEVK6XB7uemEP10btYWHbW6hz7xrSJyYeCClwIURIefStQroaj/KY6RnImAHnP2R0pJAlUyhCiJDxTn4NL24vZ2Pa37HYXXDdX8EcaXSskCUFLoQICTWtdh54JZ9HkjeQ3bbT/6HliDOMjhXSZApFCGE4r0/zw9V7OdN7mJsd/4DJV8HMbxkdK+T1u8CVUhFKqT1Kqbe6r49TSm1TSpUopVYrpeTfOUKIU/L05o/Zf6Sav8U9jYpNhyuekCWD/fBlRuB3A0XHXf8v4A9a6zOAZuCWQAYTQgwP+4628Pt1h1ie9hKxnRVw7TMQlWR0rLDQrwJXSmUCi4Hl3dcVcAGwpvsuK4GrgxFQCDF0dTg93P3iHq6P3sX8tndQX7kXshcYHSts9HcE/kfgPsDXfT0FaNFae7qvVwKjT/SLSqllSqmdSqmdDQ0NAworhBhafvFGAZ6mCn5pegZGnw25DxodKayctMCVUpcD9VrrXafyBFrrZ7TWOVrrnNTU4b35uhDiE2/uq+aVXRW8mLoCMz7/LoMRFqNjhZX+LCM8F7hSKXUZYAPigSeARKWUuXsUnglUBS+mEGIoqWzu4qev5vNoyjoy2/bA1U9B8mlGxwo7Jx2Ba60f1Fpnaq2zgRuA97XW3wQ2Al/rvtvNwOtBSymEGDJ6lgxO1YdZ2rUKpl4HZ91gdKywNJB14PcD9yqlSvDPif81MJGEEEPZnzeWUFRWxV9inkLFj/bv8S1LBk/JlzoSU2u9CdjU/f0RYE7gIwkhhqpd5c08seEwL6S9RGx7FdzwDkQlGh0rbMmRmEKIQdHucHPP6j3cFLOdOW1r4bz7YMw8o2OFNSlwIcSgePj1AkwtFTzEcsiaC+f9xOhIYU82sxJCBN1re6p4Y08FH6T+lQiXgmv/AhFSPwMl76AQIqgqGrt46LUD/DrlXUa17/dvEZs01uhYQ4JMoQghgsbj9XHP6j3MVMV8vesFmH4DTPvayX9R9IuMwIUQQfOn90soqajio+SnUNYxcNlvjY40pEiBCyGCYntpE//7/iFeTnuR6PY6WLoObPFGxxpSZApFCBFwrXY3P1y9l1vjtjOzbQOc/yBk5hgda8iRAhdCBJTXp3nwlf1Y28q5Xy+HsefCgnuNjjUkyRSKECJgOpwe7nphD5uLq8lLXU6E2wzXPA2mCKOjDUlS4EKIgKhqsXPL33dwuL6D1yZvJv3IAfj6SkjMMjrakCUFLoQYsD0VzXz32V24PG42ztzMmILlMPNGmCIn6gomKXAhxIC8tb+aH/1zH1lx8OqYfxBX8DbMuhkW/7fR0YY8KXAhxCnRWvM/75fw+/WHuDBT81TEbzEf2QcX/QrO+YFsETsIpMCFEF+a0+PlgZfzeXVPFT+YZOfHx36OcrTCDc/DxMuMjjdsSIELIb6Uxg4nt/1jFzvLm/nfs2tZfOjnKFsCfOddyJhudLxhRQpcCNFvh+va+c7KHdS3OXh79j6m5P8GRs2AG16A+Ayj4w07UuBCiH754HAD339uN9FmTd6UNxmR/zxMugKueQYio42ONyxJgQshTuofH5XzizcKmDkCnkv4P2wHP/AfXXnBz8EkB3QbRQpcCPG5vD7NY28XsiKvjOtP9/Brx6OYqsrg6idhxlKj4w17UuBCiBPqOSz+/eJ6fjG9lZuP/gyFhpteh+xzjY4nkAIXQpxAZXMXt67cyeH6DlbNPsK5Bb+EpGxYuhpSTjc6nugmBS6E6OMzh8XnPwnjzoNvPAtRSUbHE8eRAhdC9PrCw+IjLEbHE58iBS6E6HNY/FezNE+a5LD4cCAFLsQwJ4fFhy8pcCGGMTksPrxJgQsxTMlh8eFPClyIYWjzoQZ+sOrTh8Vf6T/9mRwWHzakwIUYZuSw+KFDClyIYUIOix965K9bIYaBDqeHW1fuYEVeGb+Y3srjTfdg6jrmPyxeyjuoChoL+M9t/4nb5w74Y8sIXIghTg6LH3xun5sN5RtYVbSKvQ17iTZHc80Z1zApZVJAn0cKXIghTA6LH1xNjibWHFrD6uLV1NvryYrL4v7Z93P1GVcTGxkb8OeTAhdiiJLD4gdPUWMRzxc/z7+O/AuXz8X8UfN5ZP4jLBi9AJMK3kz1SQtcKZUFPAukAxp4Rmv9hFIqGVgNZANlwDe01s1BSyqE6JfPHBYf8TvMR/bKYfEB5vF5eL/ifVYVrWJ3/W6izFFcM/4alk5cymmJpw1Khv6MwD3Aj7TWu5VSccAupdR64P8BG7TWjyulHgAeAO4PXlQhxMk43F4eeHk/r+2t9h8W3/gwyt4ih8UHUIujhTWH17D64GpqO2sZHTuaH+f8mGvGX0N8ZPygZjlpgWuta4Ca7u/blVJFwGjgKiC3+24rgU1IgQthCK01Gw/W89u1hyiqaZPD4oPgYNNBXih+gbeOvIXT62Ruxlx+OuennJd5HhGmCEMyfak5cKVUNjAT2Aakd5c7QC3+KZYT/c4yYBnAmDFjTjWnEOIEtNbklTTyu3UH2Xu0hTFJUbw7N5+J+x6Xw+IDwOvzsunoJlYVr2JH7Q5sETauOP0Klk5cyvik8UbH63+BK6VigZeBe7TWbeq4eTSttVZK6RP9ntb6GeAZgJycnBPeRwjx5W070sh/rz/E9tImRiXYeOLSFK5oWI5p30tyWPwAtTpbeeXwK7xY/CLVndVkxGRw79n3cu34a0mwJhgdr1e/ClwpZcFf3qu01q9031ynlMrQWtcopTKA+mCFFEJ8Yk9FM79ff4gPDh8jNc7Kby5K5brOF4n497P+DygXPgAL75fD4k9BSXMJzxc/z5sfv4nD62D2yNncN/s+FmYtxGwKvUV7/VmFooC/AkVa698f96M3gJuBx7svXw9KQiEEAAeqWvnD+kNsKK4nOSaSRy9MZ4lrDeatK8DngVk3wVd+DAmjjY4aVrw+L5srN7OqeBXbarZhjbCy+LTFLJ24lAnJE4yO94X681fKucC3gHyl1N7u236Kv7j/qZS6BSgHvhGciEIMbwdr2/nD+kO8W1BLQpSFhy5I5yb9BpHb/gIeJ5y1BBb+xH90pei3Nlcbrx5+lReKX6Cqo4r06HTunnU3142/jiRbeBzk1J9VKFuAz1s4uiiwcYQQPY40dPDH9w7z5v5qYiLN/GRhBrea38a642lwdcC0r/mnS0acYXTUsHKk9QjPFz3PGx+/gd1jZ1baLO49+14uGHNBSE6TfJHwSivEMHC0qYsnNhzmld2VWM0R3Lkgg+/Z1hO14//A0QKTr4LcByEtsPtqDGU+7WNL1RZWFa1ia/VWLCYLl427jKWTljI5ZbLR8U6ZFLgQIaK6xc7/bizhnzuOYjIpvjsvgzvj/03sju9DVyOceSmc/yBknGV01LDR4erg9Y9f5/mi56loryAtKo07Z97JdeOvIyUqxeh4AyYFLoTB6tsc/N+mj3l+WwUazY05I7k3eSvxO++Gjjo4/QI4/2eQmWN01LDQ7Ghmc+VmNh3dRF51HnaPnRmpM7hz5p0sGrsIi2no7AMjBS6EQRo7nDy9+QjPfliG26u5ftZIfpK2g6SdP4H9lTB2AXz97zB2vtFRQ15paymbjm5i09FN7G3Yi0/7SItK4/LTLufa8dcydcRUoyMGhRS4EIOstcvNXz44woq8UuxuL9eelc79o/NJ3fUAHCiHzDlw9Z9h3ELZeOpzeHwe9tbv9Zd25SbK28oBmJg8kWXTl5Gblcvk5MmoIf7+SYELMUjaHW5W5JXxlw+O0O7wcPm0dB7KLmLk7oehuMQ/t33Z72D8V6W4T6DT3UleVR6bjm5ic9VmWp2tmE1m5o6cyzcnfZPczFwyYofXtgFS4EIEWZfLw7MflvPUvz+mpcvNVyel8fAZR8ja9xisL4S0yXD9czDxcinuT6ntrO2dGtleux23z02CNYHzRp9HblYu80fND8qJEsKFFLgQQeJwe1m1rYInN5VwrMNF7pkjeGRiJePyfwTr90HKeLjurzDlWjnsvZvWmsKmwt7SLm4qBmBs/FiWTlxKblYuM9JmhN167WCRd0GIAHN5fKzeeZQ/v19CbZuD+acl8/yiBs4s+Bms2+E/YvLqp2Da1yFC/gg6vU6212zvnc+u76rHpEzMSJ3BvWffS25WLuMSxhkdMyTJ/z1CBIjH6+OV3VU8seEwVS12csYmsTzXydSDj8LaPIjPhCuegBnfHPanNGtyNPFB5Qd9lvpFmaM4d9S55Gbl8pXMr5BsSzY6ZsiTAhdigKpa7KwrqGXl1jLKGruYnpnA/5znZWbJb1DrNkJsOlz6Wzj7ZjBbjY5rCK01pW3HLfWr34tGkxadxpWnX8nCzIXMyZiDNWJ4vj+nSgpciC9Ja01xbTvrCupYV1hLQXUbAFNHx/PiFdHMLf8Tat1aiE6Bix6DnFuG5b7cn7fUb1LyJG4/63Zys3KZlDxpyC/1CyYpcCH6weP1saOsmfWF/tKubLajFJw9JomfXTqexUmVjCp6Gta/CbZEWPQwzLkNrMNnhYTL6+Jg00H2H9vPvoZ9bK3eSquzFYvJwpyRc7hx0o3kZuUyMmak0VGHDClwIT6H3eVl8+EG1hXUsaG4jpYuN5FmE185YwR3n5fJRVEHSSh/Hra/C50NEBnn3x3wnO+DLXTO2hIMWmsq2yvZf2w/+cfyyW/Ip6ipCLfPDUBqVCoLMxf2LvWLscQYnHhokgIX4jiNHU42FNezrqCODw434PT4SIiysGhiGovHW1ng243141Xw/vvg7vSX9pkXwYTLYPxFYBvcs5IPllZnKweOHfAXdkM+B44doNnZDECUOYrJKZO5cdKNTEudxrQR02SUPUikwMWwV97YybqCOtYX1rGzvAmfhtGJUSyZM4YrxniYYd9KxME/wZtbQXshLgPOugEmXgbZXxlyH0y6fW4ONR8ivyGf/GP57G/YT1lbGQAKxWkJp7EwayHTRkxjeup0zkg8Q9ZlG0TedTHsaK3Jr2r1z2cX1HGwrh2ASRnx3Hn+GVwxsonTGzehDr4Nu/P9v5Q6ERbcAxMWw6iZQ+bAG6011Z3V5Dfk946ui5qKcHqdAKTYUpiWOo0rT7+SaanTmJIyhbjIOINTix5S4GJYcHl8bCttZH2hf6Rd0+rApGDOuGQeuexMFieWk1b1NhS8DVsrAAVZc+Grj8LExZByutEvISA6XB0caDzA/ob9vSPsRkcjANYIK5OSJ/GNCd9geup0po+YTkZMhqwSCWFS4GLIane4+fehBtYX1vF+cT3tDg82i4mFZ6Zy3wVZXBh5gLiylfDhu2BvhggrnH6+//ySZ14CsWlGv4QB8fg8lLSU+Mu6+4PGI61H0GgAsuOzOXf0uUwbMY1pqdM4M+nMIbVX9nAgBS6GlPo2B+uL/KPsrSWNuLw+kqmZVcYAAA0ySURBVGMiuXTqSC47zcJ87w4iD6+E9RvB4/Av+TvzEv8o+/QLwnbZX5e7i7K2MspayyhqKmJ/w36Kmoqwe+wAJFoTmZ46nUvGXcL0EdOZMmIKCdahvVJmOJACF2FNa83HDZ2sK6xlfWEdeypaABiTHM3N88dyeaaDaR1bMB38b3jjI0BDQhac/f/8pT3mnLA5rN3r81LTWdNb1D2XpW2l1HfV997PYrIwKXkS146/1v9B44jpZMZlylTIECQFLsKGx+vjyLFOCqvbKKxpo6C6lcLqNpq7/GuPp2cm8KMLx3NlWh1jGjahit+GHUX+X06fBgvv95f2yGkhvW1rm6utT0GXtZVR2lpKRVsFLp+r935xljiyE7KZO3Iu2QnZZMdn915GRkQa+ArEYJECFyGp0+mhuLadwpo2CruLuri2HafHB0Ck2cTEkXFcPGUkZ42K5qLow6RUvgr7/gXt1aAi/KciO/tx/xrtpLEGv6K+3D43le2VvQVd3lZOaWspZW1lNDmaeu8XoSLIissiOz6bBaMX9Jb02PixpNhSZFQ9zEmBC8M1tDv7jKgLa9ooPdaJ9n/WRmK0hckZ8dx0zlgmZ8QwI6qRMa4SIuq2Qm0+bNoFzjawRPvnsSc+DGdeDNHG7mantabJ0fSZKY+ytjIq2yvxaE/vfZNtyWTHZ5Oblesv6e6izozLlA8WxeeSAheDxufTlDd19Snqguo2GtqdvffJTIpiyqh4rjprNFPTLEy3VDKi4yCqNh+q98OeQuj+YA6TBdImwZRrYMKlcFouWKIG9zVpH82OZuq66qjqqPrM3HS7q733vhaThbHxYzkj8QwuHHthnykP+UBRnAopcBEUDreXQ3XtfYq6qKaNLpcXALNJMT49jvPGpzJ5VDxnJbmYpMqJadoPtfuhOB/ySkD7p0ywJcDI6ZDzbf8c9sjpMOJMMAdvrtftc3Os6xh1XXXUdtVS31lPXVcd9V19Lz0+T5/fS4tOY1z8OC7NvrTP3PSomFFEmCKCllcMP1LgYsBaulwUVvtL2j9n3UZJQwden38OJNZqZnJGPN/IyWJyRiwzYloY5/0YS/1O/xTItnxor/nkAROy/CU95drusp4GiWMC+sFjl7urt4B7yri2s7ZPOTfaG3vXTPewRdhIi04jPSadmWkz/d9Hp5MenU5GbAbZ8dlEW4bf1rHCGFLg4qQ8Xh/17U5qWu1UtziobrFT0+rgaFMXRTVtVLc6eu87Mt7G5FHxXDQlnalpNqZbq0nvOoSp7j1/WR84AD3TCioCUifAuIWfFPXIaQOau9Za0+ps7S3m3pFyZ12fwj5+aqNHfGQ86THppEWnMSl5Um859xR2enQ68ZHx8sGhCBlS4MOc1pqmThc1rf5i7inn6u7rNS126tqdvaPpHrFWM6MTo8jJTmbKqHimp2gmmypIaC3yF/XH+fBRMfRML0TGQvpU/yZQI6dBxnRInQQW20kzurwuWpwtNDuaaXW20uzsvnQ00+JsocnR1Gfk3LOPRw+FYkTUCNKj0xkTN4bZI2f3FvPImJGkRaeRFp1GlHlw58+FGCgp8CGuw+mhpsVOVXcx+793UNNq7y3tnqV5PSIjTGQk2shIsDHv9BRGJUSRkWgjM1aRFdFMOseIsddCSznUFcDu/dBa8ckDxI70l/SZF38yX500Dkwm7B77J+XbsIcWZ4v/y+G/PL6ce8q652jCE4mxxJBkTSItOo2pI6b2TmccP2pOiUqRlRxiSFJa65PfK0BycnL0zp07B+35hjqnx0ttq4Pq7kKubrFT3V3SNa0OqlrstDv6fsBmUpAWZyMj0caoxChGJdjISIhidLyFMZFtjOQYCa56TO1V0FoJrVXQVun/vqux93E00KVMtIw4jZYRZ9CSlElzbBqt0Qk0a88nxexs6VPIDq+DzxMXGUeiNZEkaxIJ1gSSbN2Xx11PtCb2+bKEyVGUQgyEUmqX1jrnM7dLgYcGh9tLq91NS5e7+9JFi91Na5ebFrurz8+au1zUtjo51uH8zOMkRVsYlRhFRkIUoxL95TwqwcoYWxejVCNx7locrWV0tlXQ2V5NR0ctnV0NdDhb6FSKTpOiQ5noNJnotETSGRlNh9lKZ4TZ/zN8dPrcdHqdn/mAr4dCkWBN6Fu2tsQvvJ5gTZA9pYX4HJ9X4PInJoC01rQ7Pf7S7Sliu6tPKfcUcU8599zH4fad6BFBeTCZ3CTEQFyUJsamiYn1Mj3VR3yMl2ibh6iIdiJ1E8rThN3ZRKezlU5XO+XNXRQ2OunQXroUdJhMuD/9AZwZiI8AUnpvUihiLTHERMYSY44hJjKGWEss6ZYYYiz+73sue4r6+NFyXGScLJcTYhBIgePfK9ru9mJ3eelyeehyeXG4vXS5/F92t/82u8tLm8NDa5eTpq5Omh2dNNu7aHN20uG00+G248OFUi4wuUG5USY3SrnB5MJs9mC1+Ii0eDBbPEQku7GZPGR039enXPi0C4924PY5cflcvaNcD9Dc/QWAs/vrODafjxifJlb7iFZmYk1WMiITiI2MI8aaSExUMrExacTEZBAbm06MJba3nI8v5ihzlKy0ECIMhEWBOz1u2pwOWh1dtDsctDkddLgcdDi7v1wO7G4XXW4nXW4ndrcTu8eJw+PE6XXh9LhweV04fW7cXhdunxuPz4VHu/H43GjlAeVBKW+fy97vTT3fd1+auueVTUBM9xdwsvUUVmXGZjJjw4QNhU2DTfuwubzYfB5sHjc2jxObz4tNa2w+7b/U2n8/nyYKE9bIWGKikomJGUls/Ghi4rOISRqHOXEMxI/2n/IrIiz+0wohBmBAf8qVUpcATwARwHKt9eMBSfUp5z93E+3qwMAeJML/pSxmTJiJwIJNmTGbLJiVBbMpEovJQmRENJEmCzaTGWtEBDZlIsoUgU2BzaSIURDt82HzurF5XNjcTmxuBza3HauzgyhnBzZHGzZnBzafr7eArVrT5yRckbEQlQRRif7L6O7L3q9PX0/y710dGRPSO+kJIQbPKRe4UioC+DPwVaAS2KGUekNrXRiocD0uH3clFa1nY7NEYjNbiTZHEm02ExthIs4EMcpHbIT/MkZ5idZerF4PFo+TSI+bSK+TSLcDi9uBctvB3eX/cnWCswtcLcfd1n35OR/Q9X0TTP5S7S3ZUZCc+NnS/UwRJwT1EHAhxPAwkBH4HKBEa30EQCn1InAVEPAC/2nbNij79yfl6ur0nx38y4iI9O9WZ4mGyJ7LGH+ZxmX4vz/Rzy3R/g2Ser63xX9SxJFxQ+bktkKI8DOQAh8NHD3ueiUw99N3UkotA5YBjBkz5tSeKTELRp/9OQUbBZaYT277vJ/LnLAQYogJeqtprZ8BngH/OvBTepCv/CiQkYQQYkgYyL//q4Cs465ndt8mhBBiEAykwHcA45VS45RSkcANwBuBiSWEEOJkTnkKRWvtUUrdAazFv0jvb1rrgoAlE0II8YUGNAeutf4X8K8AZRFCCPElyBo4IYQIU1LgQggRpqTAhRAiTEmBCyFEmBrUEzoopRqA8lP89RHAsQDGCXfyfnxC3ou+5P3oayi8H2O11qmfvnFQC3wglFI7T3RGiuFK3o9PyHvRl7wffQ3l90OmUIQQIkxJgQshRJgKpwJ/xugAIUbej0/Ie9GXvB99Ddn3I2zmwIUQQvQVTiNwIYQQx5ECF0KIMBUWBa6UukQpdVApVaKUesDoPEZRSmUppTYqpQqVUgVKqbuNzhQKlFIRSqk9Sqm3jM5iNKVUolJqjVKqWClVpJQ6x+hMRlFK/bD7z8kBpdQLSimb0ZkCLeQL/LiTJ18KTAaWKKUmG5vKMB7gR1rrycA84AfD+L043t1AkdEhQsQTwLta64nAWQzT90UpNRq4C8jRWk/Fv+X1DcamCryQL3COO3my1toF9Jw8edjRWtdorXd3f9+O/w/naGNTGUsplQksBpYbncVoSqkE4DzgrwBaa5fWusXYVIYyA1FKKTMQDVQbnCfgwqHAT3Ty5GFdWgBKqWxgJrDN2CSG+yNwH+AzOkgIGAc0ACu6p5SWK6VijA5lBK11FfA7oAKoAVq11uuMTRV44VDg4lOUUrHAy8A9Wus2o/MYRSl1OVCvtd5ldJYQYQZmAU9qrWcCncCw/MxIKZWE/1/q44BRQIxS6kZjUwVeOBS4nDz5OEopC/7yXqW1fsXoPAY7F7hSKVWGf2rtAqXUc8ZGMlQlUKm17vlX2Rr8hT4cXQiUaq0btNZu4BVgvsGZAi4cClxOntxNKaXwz28Waa1/b3Qeo2mtH9RaZ2qts/H/f/G+1nrIjbL6S2tdCxxVSk3ovmkRUGhgJCNVAPOUUtHdf24WMQQ/0B3QOTEHg5w8uY9zgW8B+Uqpvd23/bT73KRCANwJrOoe7BwBvm1wHkNorbcppdYAu/Gv3trDEDykXg6lF0KIMBUOUyhCCCFOQApcCCHClBS4EEKEKSlwIYQIU1LgQggRpqTAhRAiTEmBCyFEmPr/jJUlEGIzmy4AAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.expm1(x), label=\"expm1\")\n",
        "plt.plot(np.exp(x)-1, label=\"exp-1\")\n",
        "plt.plot(np.exp2(x), label=\"exp2\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "-eYf4IuIC1DC",
        "outputId": "5af60200-3185-49d2-8815-725bb44a0f8d"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.expm1(x), label=\"expm1\")\n",
        "plt.plot(np.exp(x)-1, label=\"exp-1\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "ZLfwscDbC1Ah",
        "outputId": "18fc90a5-def8-4a96-b0ca-2385c17e66e3"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.exp(x), label=\"exp-1\")\n",
        "plt.plot(np.expm1(x), label=\"expm1\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "VrUHFymIC0-K",
        "outputId": "6ba786f9-4ea8-42c7-e945-11b57ed4d402"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.exp(x)-1, label=\"exp-1\")\n",
        "plt.plot(np.expm1(x), label=\"expm1\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "whPFxv2lC07i",
        "outputId": "5aa9f868-4f2e-48d6-8c3d-22684a69407f"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "LqztoHrHC05o"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "np.log(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rSJh1LSdC02x",
        "outputId": "f1f45dba-fead-49f2-f830-08290ae35433"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-26-de666c833898>:1: RuntimeWarning: divide by zero encountered in log\n",
            "  np.log(x)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([       -inf, -0.69314718,  0.        ,  0.40546511,  0.69314718,\n",
              "        0.91629073,  1.09861229,  1.25276297,  1.38629436,  1.5040774 ])"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = x[1:]"
      ],
      "metadata": {
        "id": "4GESnsc4DgoL"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H8ALqoQEDrOV",
        "outputId": "b1ed7db9-c5e4-4a1c-d714-2c18592cb5ce"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.log(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_4FbEOCfDr1O",
        "outputId": "e689d01f-4ce0-404f-80be-8a0570e87735"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.69314718,  0.        ,  0.40546511,  0.69314718,  0.91629073,\n",
              "        1.09861229,  1.25276297,  1.38629436,  1.5040774 ])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.log1p(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Hw8eX2OnDtTl",
        "outputId": "e8a6486f-a988-4ad9-aef8-ebbf88972deb"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.40546511, 0.69314718, 0.91629073, 1.09861229, 1.25276297,\n",
              "       1.38629436, 1.5040774 , 1.60943791, 1.70474809])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.log2(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a-YL04Y4DwBg",
        "outputId": "0ac45c0d-698e-4059-d890-375900f23a52"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.        ,  0.        ,  0.5849625 ,  1.        ,  1.32192809,\n",
              "        1.5849625 ,  1.80735492,  2.        ,  2.169925  ])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.log10(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z7u76WcwDxzs",
        "outputId": "a48ffde5-e882-4e5f-89f0-dd6a4e93b8c2"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-0.30103   ,  0.        ,  0.17609126,  0.30103   ,  0.39794001,\n",
              "        0.47712125,  0.54406804,  0.60205999,  0.65321251])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.plot(np.log(x), label=\"log\")\n",
        "plt.plot(np.log1p(x), label=\"log1p\")\n",
        "plt.plot(np.log2(x), label=\"log2\")\n",
        "plt.plot(np.log10(x), label=\"log10\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "F8F8XyUoDy-a",
        "outputId": "45d16947-6198-4921-b193-9884fd3389a0"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "p27ljhqhEJfX"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}