56^{x+7}=89^{x-10}

解答

5 \cdot 6^{x + 7} = 8 \cdot 9^{x - 10}

x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

十进制

x = 83.96421 \dots

求解步骤

5 \cdot 6^{x + 7} = 8 \cdot 9^{x - 10}

使用指数运算法则

ln (5) + (x + 7) ln (6) = ln (8) + (x - 10) ln (9)

解

ln (5) + (x + 7) ln (6) = ln (8) + (x - 10) ln (9) : x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

x = \frac{20 ln ( 3 ) + 7 ln ( 6 ) + ln ( 5 ) - 3 ln ( 2 )}{ln ( \frac{3}{2} )}

so l v e f or x, e^{3 x} = 5

5 \cdot 7^{2 y} = 175

4^{3 x - 2} = 7^{x + 3}

3^{2 x + 1} = 243

so l v e f or x, 93 = 2 3^{x}