20(10^{0.1t})=25(10^{0.05t})

解

20 (1 0^{0.1 t}) = 25 (1 0^{0.05 t})

t = \frac{ln ( \frac{5}{4} )}{0.05 ln ( 10 )}

十進法表記

t = 1.93820 \dots

解答ステップ

20 (1 0^{0.1 t}) = 25 (1 0^{0.05 t})

指数の規則を適用する

ln (20) + 0.1 t ln (10) = ln (25) + 0.05 t ln (10)

解く

ln (20) + 0.1 t ln (10) = ln (25) + 0.05 t ln (10) : t = \frac{ln ( \frac{5}{4} )}{0.05 ln ( 10 )}

t = \frac{ln ( \frac{5}{4} )}{0.05 ln ( 10 )}