Answer
$x=3$
Work Step by Step
$\log_{8}(x+5)-\log_{8}(x-2)=1$
Combine the subtraction on the left side as the logarithm of a division:
$\log_{8}\dfrac{x+5}{x-2}=1$
Rewrite this equation in exponential form:
$\dfrac{x+5}{x-2}=8^{1}$
$\dfrac{x+5}{x-2}=8$
Solve for $x$:
$x+5=8(x-2)$
$x+5=8x-16$
$x-8x=-16-5$
$-7x=-21$
$x=\dfrac{-21}{-7}$
$x=3$