25^x+5^{1+2x}=40

解答

2 5^{x} + 5^{1 + 2 x} = 40

x = \frac{ln ( \frac{20}{3} )}{2 ln ( 5 )}

十进制

x = 0.58937 \dots

求解步骤

2 5^{x} + 5^{1 + 2 x} = 40

使用指数运算法则

2 x ln (5) = ln (\frac{20}{3})

解

2 x ln (5) = ln (\frac{20}{3}) : x = \frac{ln ( \frac{20}{3} )}{2 ln ( 5 )}

x = \frac{ln ( \frac{20}{3} )}{2 ln ( 5 )}

so l v e f or x, 3^{x + 1} = 3^{x} + 18

3^{2 x - 1} = 3

3^{2 + x} = 172

5^{x - 1} = 2^{2 x + 1}

3^{- 5} \cdot 3^{3} = 3^{k}