## 2019年9月27日金曜日

### 数学 - Python - 急速・緩慢に変化する関係 - 指数関数・対数関数 - 対数関数の性質 - 対数に関する不等式の証明 - 底、真数の累乗、累乗根

1. $\begin{array}{l}3{\mathrm{log}}_{4}3\\ =\frac{3{\mathrm{log}}_{2}3}{{\mathrm{log}}_{2}4}\\ =\frac{3{\mathrm{log}}_{2}3}{{\mathrm{log}}_{2}{2}^{2}}\\ =\frac{3}{2}{\mathrm{log}}_{2}3\\ <2{\mathrm{log}}_{2}3\end{array}$

2. $\begin{array}{l}\frac{1}{2}{\mathrm{log}}_{3}3\\ ={\mathrm{log}}_{3}\sqrt{3}\\ <{\mathrm{log}}_{3}\sqrt{4}\\ ={\mathrm{log}}_{3}2\\ ={\mathrm{log}}_{3}\sqrt[3]{8}\\ <{\mathrm{log}}_{3}\sqrt[3]{9}\\ ={\mathrm{log}}_{3}{3}^{\frac{2}{3}}\\ =\frac{2}{3}\end{array}$

コード

Python 3

#!/usr/bin/env python3
from sympy import pprint, symbols, log, Rational
from unittest import TestCase, main

print('26.')

class MyTestCase(TestCase):
def setUp(self):
pass

def tearDown(self):
pass

def test(self):
spam = [3 * log(3, 4) < 2 * log(3, 2),
Rational(1, 2) < log(2, 3) < Rational(2, 3)]
for o in spam:
self.assertTrue(o)

if __name__ == '__main__':
main()


$./sample26.py 26. . ---------------------------------------------------------------------- Ran 1 test in 0.013s OK$