3^{x-2}=4^{x+1}

解答

3^{x - 2} = 4^{x + 1}

x = \frac{2 ln ( 6 )}{ln ( 3 ) - 2 ln ( 2 )}

十进制

x = - 12.45652 \dots

求解步骤

3^{x - 2} = 4^{x + 1}

使用指数运算法则

(x - 2) ln (3) = (x + 1) ln (4)

解

(x - 2) ln (3) = (x + 1) ln (4) : x = \frac{2 ln ( 6 )}{ln ( 3 ) - 2 ln ( 2 )}

x = \frac{2 ln ( 6 )}{ln ( 3 ) - 2 ln ( 2 )}

5^{3 - x} = 125

so l v e f or x, 2^{x + 4} = 2^{3 x - 1}

253428 = e^{x + 3} + 2

8^{x + 1} + 8^{x - 1} = 20

4^{6 x + 4} = 3