Answer
$x=4$
Work Step by Step
Use the definition of the log function to solve for $x$. Rewrite the problem so that the base has the exponent of the opposite side and is equal to the log's number and/or variable. Then simplify the side with $x$ by factoring and then solving for $x$. The negative answer is not part of the domain.
$\log_6(x+5)+\log_6x=2$
$\log_6x(x+5)=2$
$36=x(x+5)$
$0=x^2+5x-36$
$0=(x+9)(x-4)$
$x=-9, x=4$
$x=4$
