9(5^x)=8^{x+4}

解

9 (5^{x}) = 8^{x + 4}

x = \frac{12 ln ( 2 ) - 2 ln ( 3 )}{ln ( 5 ) - 3 ln ( 2 )}

十進法表記

x = - 13.02232 \dots

解答ステップ

9 (5^{x}) = 8^{x + 4}

指数の規則を適用する

ln (9) + x ln (5) = (x + 4) ln (8)

解く

ln (9) + x ln (5) = (x + 4) ln (8) : x = \frac{12 ln ( 2 ) - 2 ln ( 3 )}{ln ( 5 ) - 3 ln ( 2 )}

x = \frac{12 ln ( 2 ) - 2 ln ( 3 )}{ln ( 5 ) - 3 ln ( 2 )}