Answer
$x = 9998$
Work Step by Step
$\log (10x+20) = 5$
$\log_{10} (10x+20) = 5$
$10^{5} = 10x+20$
$100000 = 10x+20$
$99980 = 10x$
$x = 9998$
Check:
$\log (10(9998)+20) \overset{?}{=} 5$
$\log (99980+20) \overset{?}{=} 5$
$\log (100000) \overset{?}{=} 5$
$10^{5} \overset{?}{=} 100000$
$100000 = 100000$