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受欢迎的代数 >

(log_{5}(x))^2+5log_{5}(x)+6=0

解答

(lo g_{5} (x))^{2} + 5 lo g_{5} (x) + 6 = 0

解答

x = \frac{1}{25}, x = \frac{1}{125}

+1

十进制

x = 0.04, x = 0.008

求解步骤

(lo g_{5} (x))^{2} + 5 lo g_{5} (x) + 6 = 0

用

lo g_{5} (x) = u

改写方程式

(u)^{2} + 5 u + 6 = 0

解

u^{2} + 5 u + 6 = 0 : u = - 2, u = - 3

u = - 2, u = - 3

代回

u = lo g_{5} (x)

，求解

x

解

lo g_{5} (x) = - 2 : x = \frac{1}{25}

解

lo g_{5} (x) = - 3 : x = \frac{1}{125}

x = \frac{1}{25}, x = \frac{1}{125}

验证解:

x = \frac{1}{25}

真

, x = \frac{1}{125}

真

解为

x = \frac{1}{25}, x = \frac{1}{125}

作图

流行的例子

0.001=(ln(x))/x

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

56x^6ln(x)+15x^6=0

56 x^{6} ln (x) + 15 x^{6} = 0

lo g_{5} (2 x) = 3

ln (w) = - 0.9444

log_{1/5}(2x-3)=-1

lo g_{\frac{1}{5}} (2 x - 3) = - 1