Solving log equations

Question

I had the problem of expressing $log_9(y)=\frac{x+4}{2}$ in the form $y=k.a^x$. I got this far:

$2log_9(\frac{y}{81})=x$

and was wondering if it is valid to draw the conclusion that $\frac{y}{81}=2(9^x)$, whichwould make $k=162$ and $a=9$.

Answer 1

$$log_9(y)=\frac{x+4}{2}$$

$$9^\frac{x+4}{2} = y$$

$$3^{x+4} = y$$

$$81*3^x = y$$