solution: We are asked to solve $4^x=8$ for $x$.  Writing $4$ as $2^2$ and $8$ as $2^3$, the equation becomes $(2^2)^x=2^3$.  The left-hand side simplifies to $2^{2x}$, so we may set exponents equal to find $2x=3$, which implies $x=\boxed{\frac{3}{2}}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  What power of 4 is equal to 8? Express your answer as a common fraction.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: \frac{3}{2}
extra_info.question: What power of 4 is equal to 8? Express your answer as a common fraction.
extra_info.split: test