5^{x+1}=100(3)^x

解

5^{x + 1} = 100 (3)^{x}

x = \frac{ln ( 20 )}{ln ( 5 ) - ln ( 3 )}

十進法表記

x = 5.86449 \dots

解答ステップ

5^{x + 1} = 100 (3)^{x}

指数の規則を適用する

(x + 1) ln (5) = ln (100) + x ln (3)

解く

(x + 1) ln (5) = ln (100) + x ln (3) : x = \frac{ln ( 20 )}{ln ( 5 ) - ln ( 3 )}

x = \frac{ln ( 20 )}{ln ( 5 ) - ln ( 3 )}