solution: Since the prime factorization of 72 is $72=2^3\cdot 3^2$, we have $x=\boxed{2}$.
prompt.content: <|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
  
prompt.role: user
extra_info.answer: 2
extra_info.question: For what value of $x$ is $2^3\cdot3^x=72$?
extra_info.split: test