10e^{2x}=7*2^{ax}

解答

10 e^{2 x} = 7 \cdot 2^{a x}

x = \frac{ln ( 7 ) - ln ( 10 )}{2 - ln ( 2 ) a}

求解步骤

10 e^{2 x} = 7 \cdot 2^{a x}

使用指数运算法则

ln (10) + 2 x = ln (7) + a x ln (2)

解

ln (10) + 2 x = ln (7) + a x ln (2) : x = \frac{ln ( 7 ) - ln ( 10 )}{2 - ln ( 2 ) a}

x = \frac{ln ( 7 ) - ln ( 10 )}{2 - ln ( 2 ) a}

216 = 6^{x}

4^{x} = 8^{12}

2^{- 2 (4 + x)} = 2^{x - 1}

e^{5 - 4 x} = 2

(\frac{2}{3})^{x} = 8