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受欢迎的代数 >

4^t+6^t=9^t

解答

4^{t} + 6^{t} = 9^{t}

解答

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

+1

十进制

t = 1.18681 \dots

求解步骤

4^{t} + 6^{t} = 9^{t}

两边除以

4^{t}

\frac{4 ^{t}}{4 ^{t}} + \frac{6 ^{t}}{4 ^{t}} = \frac{9 ^{t}}{4 ^{t}}

化简

1 + (\frac{3}{2})^{t} = (\frac{9}{4})^{t}

使用指数运算法则

1 + (\frac{3}{2})^{t} = ((\frac{3}{2})^{t})^{2}

用

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

改写方程式

1 + u = (u)^{2}

解

1 + u = u^{2} : 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})^{t}

，求解

t

解

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

解

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

无解

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

作图

流行的例子

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3^{3 - x} = x

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9^{(x-1)/2}=(3^x)^2

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