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

+1

十进制

x = 20.08553 \dots, x = 0.36787 \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 = 3, u = - 1

u = 3, u = - 1

代回

u = ln (x)

，求解

x

解

ln (x) = 3 : x = e^{3}

解

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

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

验证解:

x = e^{3}

真

, x = \frac{1}{e}

真

解为

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

作图

流行的例子

log_{3}(x+17)-2=log_{3}(2x)

lo g_{3} (x + 17) - 2 = lo g_{3} (2 x)

4=(ln(2x))/(ln(4x))

4 = \frac{ln ( 2 x )}{ln ( 4 x )}

2 lo g_{2} (x) = 4

solvefor t,x=ln(t)

so l v e f or t, x = ln (t)

lo g_{2} (x^{2}) = 4