27^{3x-7}=9^{6x-1}

解答

2 7^{3 x - 7} = 9^{6 x - 1}

x = - \frac{19}{3}

求解步骤

2 7^{3 x - 7} = 9^{6 x - 1}

使用指数运算法则

3 (3 x - 7) = 2 (6 x - 1)

解

3 (3 x - 7) = 2 (6 x - 1) : x = - \frac{19}{3}

x = - \frac{19}{3}

6 4^{2 x + 4} = 1 6^{5 x}

2^{x + 3} \cdot 2^{- 3 x + 3} = 2

2 7^{x} = \frac{1}{3}

3^{x - 1} = 2

3 = 4^{x}