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受欢迎的代数 >

(sqrt(ln(x)))/(ln(sqrt(x)))=3

解答

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

解答

x = e^{\frac{4}{9}}

+1

十进制

x = 1.55962 \dots

求解步骤

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

在两边乘以

ln (x)

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

化简

ln (x) = 3 ln (x)

使用对数运算法则

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

用

ln (x) = u

改写方程式

u = 3 \cdot \frac{1}{2} u

解

u = 3 \cdot \frac{1}{2} u : u = \frac{4}{9}, u = 0

u = \frac{4}{9}, u = 0

代回

u = ln (x)

，求解

x

解

ln (x) = \frac{4}{9} : x = e^{\frac{4}{9}}

解

ln (x) = 0 : x = 1

x = e^{\frac{4}{9}}, x = 1

验证解:

x = e^{\frac{4}{9}}

真

, x = 1

假

解是

x = e^{\frac{4}{9}}

作图

流行的例子

log_{3}(6x-2)=2

lo g_{3} (6 x - 2) = 2

3 ln (5 x) = 10

solvefor a,x=ln(a/s)

so l v e f or a, x = ln (\frac{a}{s})

log_{1/3}(x)=-3

lo g_{\frac{1}{3}} (x) = - 3

7log_{6}(4x)+5=-2

7 lo g_{6} (4 x) + 5 = - 2