Answer
$25$
Work Step by Step
The domain of the variable requires that $x>0$ and $x-21>0$
This means that $x>21$.
Recall:
$\log_a (MN) = \log_a M+\log_a N$
Thus, the given equation is equivalent to:
$\log(x(x-21))= 2\\
\log(x^2-21x)=2$
Recall further that:
$y = \log_a b \text{ is equivalent to } b=a^y$.
Therefore,
$x^2-21x = 10^2$
$x^2-21x = 100$
$x^2-21x-100=0$
By Factoring:
$(x+4)(x-25)=0$
Using the Zero-Product Property:
$x+4=0 \hspace{5pt} \hspace{15pt} \text{or} \hspace{15pt} x-25 =0\\
x=-4 \text{ or } x=25$
Since $x>21$, then $x$ cannoe be $-4$
Hence,
$x= \boxed{25}$
