5(2^x)=3(7^{4x-4})

解

5 (2^{x}) = 3 (7^{4 x - 4})

x = \frac{4 ln ( 7 ) + ln ( 5 ) - ln ( 3 )}{4 ln ( 7 ) - ln ( 2 )}

十進法表記

x = 1.16980 \dots

解答ステップ

5 (2^{x}) = 3 (7^{4 x - 4})

指数の規則を適用する

ln (5) + x ln (2) = ln (3) + (4 x - 4) ln (7)

解く

ln (5) + x ln (2) = ln (3) + (4 x - 4) ln (7) : x = \frac{4 ln ( 7 ) + ln ( 5 ) - ln ( 3 )}{4 ln ( 7 ) - ln ( 2 )}

x = \frac{4 ln ( 7 ) + ln ( 5 ) - ln ( 3 )}{4 ln ( 7 ) - ln ( 2 )}