1. **Problem statement:** Evaluate $\log_4 64$. 2. **Recall the definition:** $\log_b a = c$ means $b^c = a$. 3. **Apply the definition:** We want to find $x$ such that $4^x = 64$. 4. **Express both sides with the same base:** $4 = 2^2$ and $64 = 2^6$. So, $$4^x = (2^2)^x = 2^{2x} = 2^6$$ 5. **Equate exponents:** $$2x = 6$$ 6. **Solve for $x$:** $$x = \frac{6}{2} = 3$$ 7. **Final answer:** $$\log_4 64 = 3$$