Answer
$x=91$
or
The solution set is: $\{91\}$
Work Step by Step
The term $125$ can be written as: $125=5^3$
So, the given equation can be equivalent to $5^{x+2}=5^3$
Recall the rule that $\log y =x \longrightarrow 10^x=y$
Applying this rule, we obtain:
$\log (x+9) =2 \\ 10^2 =x+9$
Simplify this equation to obtain:
$100=x+9 \\ 100-9=x+9-9 \\ x=91$
So, the solution set is: $\{91\}$
