### Instruction: If $4^6=8^n$, what is $n$?### Response: So we have $4^6=8^n$.
Let's write that as $4^6=2^{3n}$.
Now we can use the rule that $a^m=b^n$ can be rewritten as $\log_b(a)=\frac{m}{n}$.
So we have $\log_2(4)=\frac{6}{3n}$.
And since $\log_2(4)=2$, we have $2=\frac{6}{3n}$.
So $n=1$.