5^{3x}*2^x=sqrt(250)

解

5^{3 x} \cdot 2^{x} = 250

x = \frac{ln ( 250 )}{6 ln ( 5 ) + 2 ln ( 2 )}

十進法表記

x = 0.5

解答ステップ

5^{3 x} \cdot 2^{x} = 250

指数の規則を適用する

(lo g_{2} (5) \cdot 3 x + x) ln (2) = \frac{1}{2} ln (250)

解く

(lo g_{2} (5) \cdot 3 x + x) ln (2) = \frac{1}{2} ln (250) : x = \frac{ln ( 250 )}{6 ln ( 5 ) + 2 ln ( 2 )}

x = \frac{ln ( 250 )}{6 ln ( 5 ) + 2 ln ( 2 )}