3^{x^2-x-12}=7^{x^2-x-12}

解答

3^{x^{2} - x - 12} = 7^{x^{2} - x - 12}

x = - 3, x = 4

求解步骤

3^{x^{2} - x - 12} = 7^{x^{2} - x - 12}

使用指数运算法则

(x^{2} - x - 12) ln (3) = (x^{2} - x - 12) ln (7)

解

(x^{2} - x - 12) ln (3) = (x^{2} - x - 12) ln (7) : x = - 3, x = 4

x = - 3, x = 4

e^{6 x} - e^{3 x} - 2 = 0

4^{x - 1} = 5^{x + 1}

9^{8 x - 4} = \frac{1}{( 81 ) ^{2 x - 5}}

\frac{1}{4 ^{x - 2}} = 64

5^{a} = 1