7^{3x-4}=3^{x-5}

解答

7^{3 x - 4} = 3^{x - 5}

x = \frac{- 5 ln ( 3 ) + 4 ln ( 7 )}{3 ln ( 7 ) - ln ( 3 )}

十进制

x = 0.48333 \dots

求解步骤

7^{3 x - 4} = 3^{x - 5}

使用指数运算法则

(3 x - 4) ln (7) = (x - 5) ln (3)

解

(3 x - 4) ln (7) = (x - 5) ln (3) : x = \frac{- 5 ln ( 3 ) + 4 ln ( 7 )}{3 ln ( 7 ) - ln ( 3 )}

x = \frac{- 5 ln ( 3 ) + 4 ln ( 7 )}{3 ln ( 7 ) - ln ( 3 )}

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

0 = - e^{- x} + 3 e^{- 3 x}

2^{\frac{x}{15}} = 10

4 9^{x} \cdot 7^{x^{2}} = 240 1^{2}

2500 = 5000 e^{100 x}