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受欢迎的代数 >

-1.25ln(10-0.8x)+1.4539=3

解答

- 1.25 ln (10 - 0.8 x) + 1.4539 = 3

解答

x = \frac{- 1 + 10 e ^{\frac{1.5461}{1.25}}}{0.8 e ^{\frac{1.5461}{1.25}}}

+1

十进制

x = 12.13713 \dots

求解步骤

- 1.25 ln (10 - 0.8 x) + 1.4539 = 3

将

1.4539

到右边

- 1.25 ln (10 - 0.8 x) = 1.5461

两边除以

- 1.25

ln (10 - 0.8 x) = - \frac{1.5461}{1.25}

使用对数运算法则

10 - 0.8 x = \frac{1}{e ^{\frac{1.5461}{1.25}}}

解

10 - 0.8 x = \frac{1}{e ^{\frac{1.5461}{1.25}}} : x = \frac{- 1 + 10 e ^{\frac{1.5461}{1.25}}}{0.8 e ^{\frac{1.5461}{1.25}}}

x = \frac{- 1 + 10 e ^{\frac{1.5461}{1.25}}}{0.8 e ^{\frac{1.5461}{1.25}}}

验证解:

x = \frac{- 1 + 10 e ^{\frac{1.5461}{1.25}}}{0.8 e ^{\frac{1.5461}{1.25}}}

真

解是

x = \frac{- 1 + 10 e ^{\frac{1.5461}{1.25}}}{0.8 e ^{\frac{1.5461}{1.25}}}

作图

流行的例子

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ln (8 w - 6) = ln (6 w)

0=20log_{10}(3x)

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