Answer
The solution set is $\{22\}$.
Work Step by Step
The given equation is
$\log (x-2) + \log 5 = \log 100$
Use product rule.
$\log (x-2)^5 = \log 100$
$ (x-2)^5 = 100$
Divide both sides by $5$.
$ \frac{(x-2)5}{5} = \frac{100}{5}$
Simplify.
$x-2 = 20$
Add $2$ to both sides
$x-2+2=20+2$.
Simplify.
$x=22$.
