100^{2/x}=(1+0.1)^x

解

10 0^{\frac{2}{x}} = (1 + 0.1)^{x}

x = \frac{2 ln ^{\frac{1}{2}} ( 10 )}{ln ^{\frac{1}{2}} ( 1.1 )}, x = - \frac{2 ln ^{\frac{1}{2}} ( 10 )}{ln ^{\frac{1}{2}} ( 1.1 )}

十進法表記

x = 9.83033 \dots, x = - 9.83033 \dots

解答ステップ

10 0^{\frac{2}{x}} = (1 + 0.1)^{x}

指数の規則を適用する

\frac{2}{x} ln (100) = x ln (1 + 0.1)

解く

\frac{2}{x} ln (100) = x ln (1 + 0.1) : x = \frac{2 ln ^{\frac{1}{2}} ( 10 )}{ln ^{\frac{1}{2}} ( 1.1 )}, x = - \frac{2 ln ^{\frac{1}{2}} ( 10 )}{ln ^{\frac{1}{2}} ( 1.1 )}

x = \frac{2 ln ^{\frac{1}{2}} ( 10 )}{ln ^{\frac{1}{2}} ( 1.1 )}, x = - \frac{2 ln ^{\frac{1}{2}} ( 10 )}{ln ^{\frac{1}{2}} ( 1.1 )}