Solve the logarithmic equation below algebraically.
$$\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )$$
A) $- 2$ and 5
B) 2 and 9
C) 5 and 9
D) $- 2$ and 9
E) 2 and 5

Question

Quizplus · Accepted Answer

To solve the equation, use the property of logarithms: $\ln a - \ln b = \ln \frac{a}{b}$. The equation becomes $\ln (x - 6) = \ln \frac{x + 6}{x - 4}$. By equating the arguments, we have $x - 6 = \frac{x + 6}{x - 4}$. Solving this equation gives the solutions $x = 2$ and $x = 9$.

Solve the Logarithmic Equation Below Algebraically ln⁡(x−6)=ln⁡(x+6)−ln⁡(x−4)\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )ln(x−6)=ln(x+6)−ln(x−4)

Solve the Logarithmic Equation Below Algebraically $\ln ( x - 6 ) = \ln ( x + 6 ) - \ln ( x - 4 )$