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受欢迎的代数 >

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

解答

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

解答

x = \frac{e + 1}{e - 1}

+1

十进制

x = 2.16395 \dots

求解步骤

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

两边加上

ln (x - 1)

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

化简

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

使用对数运算法则

x + 1 = e (x - 1)

解

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

x = \frac{e + 1}{e - 1}

验证解:

x = \frac{e + 1}{e - 1}

真

解是

x = \frac{e + 1}{e - 1}

作图

流行的例子

log_{-2x-3}(2x^2-2x-15)=2

lo g_{- 2 x - 3} (2 x^{2} - 2 x - 15) = 2

log_{10}(x)= 4/5

lo g_{10} (x) = \frac{4}{5}

log_{2}(x)=(ln(x))/(ln(2))

lo g_{2} (x) = \frac{ln ( x )}{ln ( 2 )}

ln (- 7 x - 4) = 3

log_{1/3}(4+5x)=-2

lo g_{\frac{1}{3}} (4 + 5 x) = - 2