Solve the equation.
-$$\ln x + \ln ( x - 1 ) = \ln 2$$
A)2, -1
B)-1
C) $\frac { 3 } { 2 }$
D)2

Name: Solve the equation. -\[\ln x + \ln ( x - 1 ) = \ln 2\] A)2, -1 B)-1 C) $\frac { 3 } { 2 }$ D)2
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Question

Quizplus · Accepted Answer

Using the property of logarithms, $\ln x + \ln (x - 1) = \ln (x(x - 1))$. So, $\ln (x(x - 1)) = \ln 2$. This implies $x(x - 1) = 2$. Solving $x^2 - x - 2 = 0$ gives roots $x = 2$ and $x = -1$. However, $\ln(-1)$ is undefined, so the only valid solution is $x = 2$.

Solve the Equation ln⁡x+ln⁡(x−1)=ln⁡2\ln x + \ln ( x - 1 ) = \ln 2lnx+ln(x−1)=ln2

Solve the Equation $\ln x + \ln ( x - 1 ) = \ln 2$