数学 - Python - 急速・緩慢に変化する関係 - 指数関数・対数関数 - 指数関数と対数関数 - 指数関数の性質 - 不等式の解、増加関数、減少関数

学習環境

新装版数学読本2 (松坂和夫(著)、岩波書店)の第7章(急速・緩慢に変化する関係 - 指数関数・対数関数)、7.2(指数関数と対数関数)、指数関数の性質の問12の解答を求めてみる。

1. $\begin{array}{l} 4^{x} < 32 \\ 2^{2 x} < 2^{5} \\ 2 x < 5 \\ x < \frac{5}{2} \end{array}$
2. $\begin{array}{l} 0. 2^{x} \geq 1 \\ {(\frac{1}{5})}^{x} \geq 1 \\ 5^{- x} \geq 5^{0} \\ - x \geq 0 \\ x \leq 0 \end{array}$
3. $\begin{array}{l} {(\frac{1}{3})}^{x} \leq 27 \\ 3^{- x} \leq 3^{3} \\ - x \leq 3 \\ x \geq - 3 \end{array}$
4. $\begin{array}{l} 0.125 < 0. 5^{x} < 1 \\ {(0.5)}^{3} < 0. 5^{x} < 0. 5^{0} \\ 0 < x < 3 \end{array}$

#!/usr/bin/env python3 from sympy import pprint, symbols, sqrt, root, Rational, plot from sympy.solvers.inequalities import reduce_inequalities print('12.') x = symbols('x') inequalities = [4 ** x > 32, 0.2 ** x >= 1, Rational(1, 3) ** x <= 27, (0.125 < 0.5 ** x, 0.5 ** x < 1)] for i, inequality in enumerate(inequalities, 1): print(f'({i})') try: pprint(reduce_inequalities(inequality, x).expand()) except Exception as err: pprint(reduce_inequalities(inequality, x)) print() fss = [((4 ** x, 32), (0, 35)), ((0.2 ** x, 1), (0, 2)), ((Rational(1, 3) ** x, 27), (0, 30)), ((0.125, 0.5 ** x, 1), (0, 2))] for i, (fs, (y1, y2)) in enumerate(fss, 1): p = plot(*fs, ylim=(y1, y2), legend=True, show=False) colors = ['red', 'green', 'blue', 'brown', 'orange', 'purple', 'pink', 'gray', 'skyblue', 'yellow'] for s, color in zip(p, colors): s.line_color = color p.show() p.save(f'sample12_{i}.png')

入出力結果(Bash、cmd.exe(コマンドプロンプト)、Terminal、Jupyter(IPython))