Answer
See below.
Work Step by Step
a) We know that if $a^x=y$, then $\log_a y=x$ and vice versa. Hence here $4^2=x-2\\16=x-2\\x=18$
b) Since the logarithm function is increasing (because $x$ has a positive coefficient and the base is larger than $1$), the solutions, using a), will be $2\lt x\leq18$ (also because $x-2\gt0\\x\gt2$)
