e^{2x}=3e^{-1/4 x}

解答

e^{2 x} = 3 e^{- \frac{1}{4} x}

x = \frac{4 ln ( 3 )}{9}

十进制

x = 0.48827 \dots

求解步骤

e^{2 x} = 3 e^{- \frac{1}{4} x}

使用指数运算法则

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

解

2 x = ln (3) - \frac{1}{4} x : x = \frac{4 ln ( 3 )}{9}

x = \frac{4 ln ( 3 )}{9}

\frac{a ^{20}}{a ^{x}} = a^{3}

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

3^{x} = \frac{1}{27}

so l v e f or x, 5^{x + y} = 125

e^{x + 2} = 15