Answer
$\{91\}$
Work Step by Step
We know that if $\log{y}=x$ then $10^x=y$.
Hence,
$\log{(x+9)}=2 \longrightarrow 10^2=x+9$
Solve the equarton above to obtain
$100=x+9\\
100-9=x+9-9\\
91=x$
The solution set is: $\{91\}.$