15.7(0.98)^x=11(0.99)^x

解

15.7 (0.98)^{x} = 11 (0.99)^{x}

x = \frac{ln ( 15.7 ) - ln ( 11 )}{ln ( 0.99 ) - ln ( 0.98 )}

十進法表記

x = 35.04259 \dots

解答ステップ

15.7 (0.98)^{x} = 11 (0.99)^{x}

指数の規則を適用する

ln (15.7) + x ln (0.98) = ln (11) + x ln (0.99)

解く

ln (15.7) + x ln (0.98) = ln (11) + x ln (0.99) : x = \frac{ln ( 15.7 ) - ln ( 11 )}{ln ( 0.99 ) - ln ( 0.98 )}

x = \frac{ln ( 15.7 ) - ln ( 11 )}{ln ( 0.99 ) - ln ( 0.98 )}