5^{2x}=8^{x-1}

解答

5^{2 x} = 8^{x - 1}

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

十进制

x = - 1.82497 \dots

求解步骤

5^{2 x} = 8^{x - 1}

使用指数运算法则

2 x ln (5) = (x - 1) ln (8)

解

2 x ln (5) = (x - 1) ln (8) : x = - \frac{3 ln ( 2 )}{2 ln ( 5 ) - 3 ln ( 2 )}

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

so l v e f or x, 2 e^{2 x} - e^{x} = 0

300 \cdot 2^{0.02 x} = 9000

87.88 e^{3 r} = 263.64

7 \cdot 1 0^{x} - 49 = 0

e^{2 x} - 2 \cdot e^{x} - 3 = 0