If $2^{x-3}=4^2$, find $x$.
I know that $4^2$ is the same as $2^4$, so I can rewrite the equation as $2^{x-3}=2^4$. Now I have the same base on both sides, so I can use the rule that if $a^b=a^c$, then $b=c$. That means $x-3=4$, so I can add $3$ to both sides to get $x=7$. 