3^x× 5^{2x}=150

解

3^{x} \cdot 5^{2 x} = 150

x = \frac{ln ( 150 )}{ln ( 75 )}

十進法表記

x = 1.16054 \dots

解答ステップ

3^{x} \cdot 5^{2 x} = 150

指数の規則を適用する

(x + lo g_{3} (5) \cdot 2 x) ln (3) = ln (150)

解く

(x + lo g_{3} (5) \cdot 2 x) ln (3) = ln (150) : x = \frac{ln ( 150 )}{ln ( 75 )}

x = \frac{ln ( 150 )}{ln ( 75 )}