2^{2x}2=3^x3^5

解

2^{2 x} \cdot 2 = 3^{x} \cdot 3^{5}

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

十進法表記

x = 16.68478 \dots

解答ステップ

2^{2 x} \cdot 2 = 3^{x} \cdot 3^{5}

指数の規則を適用する

(2 x + 1) ln (2) = (x + 5) ln (3)

解く

(2 x + 1) ln (2) = (x + 5) ln (3) : x = \frac{5 ln ( 3 ) - ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

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