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受欢迎的代数 >

ln(x+1)-ln(x-4)=ln(x)

解答

ln (x + 1) - ln (x - 4) = ln (x)

解答

x = \frac{5 + 29}{2}

+1

十进制

x = 5.19258 \dots

求解步骤

ln (x + 1) - ln (x - 4) = ln (x)

两边加上

ln (x - 4)

ln (x + 1) - ln (x - 4) + ln (x - 4) = ln (x) + ln (x - 4)

化简

ln (x + 1) = ln (x) + ln (x - 4)

使用对数运算法则

x + 1 = x (x - 4)

解

x + 1 = x (x - 4) : x = \frac{5 + 29}{2}, x = \frac{5 - 29}{2}

x = \frac{5 + 29}{2}, x = \frac{5 - 29}{2}

验证解:

x = \frac{5 + 29}{2}

真

, x = \frac{5 - 29}{2}

假

解是

x = \frac{5 + 29}{2}

作图

流行的例子

log_{10}(x+2)+log_{10}(2x)=1

lo g_{10} (x + 2) + lo g_{10} (2 x) = 1

L(v)=vln(1-v^2)

L (v) = v ln (1 - v^{2})

lo g_{b} (81) = 2

log_{10}(x^2-16x+1)=0

lo g_{10} (x^{2} - 16 x + 1) = 0

2 ln (3 x^{2} + 1) = 13