Answer
$ x= 5$
Work Step by Step
We are given that $\log x+\log (x+15)=2$
Use rule: $\log_b{p \cdot q} =\log p + \log q $
$\log [ x(x+15)]=100$
or, $ x^2+15 x-100 =0$
or, $(x-5)(x+20)=0$
Simplify it by equating both factors to $0$:
$ x -5 =0 \implies x =5$
and $ x +20 =0 \implies x=-20$
But negative values cannot be considered (because we can not take the log of a negative number).
So, the result is: $ x= 5$
