Since the prime factorization of 72 is $72=2^3\cdot 3^2$, we have $x=\boxed{2}$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For what value of $x$ is $2^3\cdot3^x=72$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2
For what value of $x$ is $2^3\cdot3^x=72$?
test