5^{x+2}=4^{2x-2}

解答

5^{x + 2} = 4^{2 x - 2}

x = \frac{2 ln ( 20 )}{4 ln ( 2 ) - ln ( 5 )}

十进制

x = 5.15106 \dots

求解步骤

5^{x + 2} = 4^{2 x - 2}

使用指数运算法则

(x + 2) ln (5) = (2 x - 2) ln (4)

解

(x + 2) ln (5) = (2 x - 2) ln (4) : x = \frac{2 ln ( 20 )}{4 ln ( 2 ) - ln ( 5 )}

x = \frac{2 ln ( 20 )}{4 ln ( 2 ) - ln ( 5 )}

e^{e} - 12 e^{- x} - 1 = 0

5 = 10 (0.8)^{x}

2 7^{x} = 9^{x - 4}

5. 3^{x} + 2. 3^{3} = 63

4 e^{2 x} = 81 - 5 e^{2 x}