Answer
$x=5$
Work Step by Step
Combine like terms. Then use the definition of the log function to rearrange the logarithm. Then factor the side with $x$ and solve. $-20$ is not part of the domain, so $5$ is the only answer.
$\log x+\log(x+15)=2$
$\log x(x+15)=2$
$100=x^2+15x$
$x^2+15x-100=0$
$(x-5)(x+20)=0$
$x=5, x=-20$
$x=5$
