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受欢迎的代数 >

ln(x)-3/(ln(x))=-2

解答

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

解答

x = e, x = \frac{1}{e ^{3}}

+1

十进制

x = 2.71828 \dots, x = 0.04978 \dots

求解步骤

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

在两边乘以

ln (x)

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

化简

ln (x) ln (x) - \frac{3}{ln ( x )} ln (x) : ln^{2} (x) - 3

ln^{2} (x) - 3 = - 2 ln (x)

用

ln (x) = u

改写方程式

u^{2} - 3 = - 2 u

解

u^{2} - 3 = - 2 u : u = 1, u = - 3

u = 1, u = - 3

代回

u = ln (x)

，求解

x

解

ln (x) = 1 : x = e

解

ln (x) = - 3 : x = \frac{1}{e ^{3}}

x = e, x = \frac{1}{e ^{3}}

验证解:

x = e

真

, x = \frac{1}{e ^{3}}

真

解为

x = e, x = \frac{1}{e ^{3}}

作图

流行的例子

lo g_{e} (x) = 0

log_{x}(1/64)=-2

lo g_{x} (\frac{1}{64}) = - 2

lo g_{2} (x + 4) = 3

log_{6}((5x-9)^2)=4

lo g_{6} ((5 x - 9)^{2}) = 4

lo g_{x} (5) = 3