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受欢迎的代数 >

(ln(x^3))/4 =(ln(x))^3

解答

\frac{ln ( x ^{3} )}{4} = (ln (x))^{3}

解答

x = 1, x = \frac{1}{e ^{\frac{3}{2}}}, x = e^{\frac{3}{2}}

+1

十进制

x = 1, x = 0.42062 \dots, x = 2.37744 \dots

求解步骤

\frac{ln ( x ^{3} )}{4} = (ln (x))^{3}

在两边乘以

4

\frac{ln ( x ^{3} )}{4} \cdot 4 = (ln (x))^{3} \cdot 4

化简

ln (x^{3}) = 4 ln^{3} (x)

使用对数运算法则

3 ln (x) = 4 ln^{3} (x)

用

ln (x) = u

改写方程式

3 u = 4 u^{3}

解

3 u = 4 u^{3} : u = 0, u = - \frac{3}{2}, u = \frac{3}{2}

u = 0, u = - \frac{3}{2}, u = \frac{3}{2}

代回

u = ln (x)

，求解

x

解

ln (x) = 0 : x = 1

解

ln (x) = - \frac{3}{2} : x = \frac{1}{e ^{\frac{3}{2}}}

解

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

x = 1, x = \frac{1}{e ^{\frac{3}{2}}}, x = e^{\frac{3}{2}}

验证解:

x = 1

真

, x = \frac{1}{e ^{\frac{3}{2}}}

真

, x = e^{\frac{3}{2}}

真

解为

x = 1, x = \frac{1}{e ^{\frac{3}{2}}}, x = e^{\frac{3}{2}}

作图

流行的例子

log_{5}(x^2-2x-10)=2

lo g_{5} (x^{2} - 2 x - 10) = 2

ln (x^{2}) - 1 = 0

log_{10}(x)-2log_{10}(5x)=2

lo g_{10} (x) - 2 lo g_{10} (5 x) = 2

x^{1+log_{5}(x)}=25x^2

x^{1 + l o g_{5} (x)} = 25 x^{2}

log_{10}(x+3)=1-log_{10}(x)

lo g_{10} (x + 3) = 1 - lo g_{10} (x)