If $\frac{9^n\cdot3^{2n+1}}{81}=243$, find $n$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $\frac{9^n\cdot3^{2n+1}}{81}=243$, find $n$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
If $\frac{9^n\cdot3^{2n+1}}{81}=243$, find $n$.
train