Answer
$x=3$
Work Step by Step
$\log_{3}(x+15)-\log_{3}(x-1)=2$
Combine the logarithms on the left side of the equation as a division:
$\log_{3}\Big(\dfrac{x+15}{x-1}\Big)=2$
Write this equation in exponential form:
$\dfrac{x+15}{x-1}=3^{2}$
$\dfrac{x+15}{x-1}=9$
Solve for $x$:
$x+15=9(x-1)$
$x+15=9x-9$
$x-9x=-9-15$
$-8x=-24$
$x=\dfrac{-24}{-8}=3$
