Solve: $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$
A) $\left\{ \frac { 17 } { 5 } \right\}$
B) $\left\{ \frac { 9 } { 5 } \right\}$
C) $\{ - 3 \}$
D) no solution

Question

Quizplus · Accepted Answer

Using the logarithm property $\log a - \log b = \log \left(\frac{a}{b}\right)$, the equation becomes $\log \left(\frac{x + 5}{x - 2}\right) = \log 6$. Since the logarithms are equal, the arguments must be equal, leading to $\frac{x + 5}{x - 2} = 6$. Solving this equation for $x$ gives $x = \frac{17}{5}$.

Solve log⁡(x+5)−log⁡(x−2)=log⁡6\log ( x + 5 ) - \log ( x - 2 ) = \log 6log(x+5)−log(x−2)=log6

Solve $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$