10^{6x-5}=8^{6x-2}

解答

1 0^{6 x - 5} = 8^{6 x - 2}

x = \frac{ln ( \frac{3125}{2} )}{6 ln ( \frac{5}{4} )}

十进制

x = 5.49275 \dots

求解步骤

1 0^{6 x - 5} = 8^{6 x - 2}

使用指数运算法则

(6 x - 5) ln (10) = (6 x - 2) ln (8)

解

(6 x - 5) ln (10) = (6 x - 2) ln (8) : x = \frac{ln ( \frac{3125}{2} )}{6 ln ( \frac{5}{4} )}

x = \frac{ln ( \frac{3125}{2} )}{6 ln ( \frac{5}{4} )}

2^{x - 3} = \frac{1}{8}

90 - 0.04 x = 30 e^{0.001 x}

5^{n} = 1

12 5^{l o g_{3} (x + 3)} = 8

e^{(2 x)} - 3 e^{x} + 2 = 0