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受欢迎的代数 >

6^x=3^{2x}-2^{2x}

解答

6^{x} = 3^{2 x} - 2^{2 x}

解答

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

+1

十进制

x = 1.18681 \dots

求解步骤

6^{x} = 3^{2 x} - 2^{2 x}

两边除以

2^{2 x}

\frac{6 ^{x}}{2 ^{2 x}} = \frac{3 ^{2 x}}{2 ^{2 x}} - \frac{2 ^{2 x}}{2 ^{2 x}}

化简

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

使用指数运算法则

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

用

(\frac{3}{2})^{x} = u

改写方程式

u = (u)^{2} - 1

解

u = u^{2} - 1 : u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

代回

u = (\frac{3}{2})^{x}

，求解

x

解

(\frac{3}{2})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

解

(\frac{3}{2})^{x} = \frac{1 - 5}{2} : x \in R

无解

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{3}{2} )}

作图

流行的例子

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