We are given the equation $f(x) = 4^x$, where $f(x)$ represents the number of bacteria after $x$ hours, and we need to solve for $x$ when $f(x) = 64$.

The equation becomes: $4^x = 64$

We can express 64 as a power of 4: $64 = 4^3$

Thus, we have: $4^x = 4^3$

Since the bases are the same, we can set the exponents equal to each other: $x = 3$

So, the correct answer is A. x = 3.

Would you like further details or have any questions? Here are some related questions you might consider:

1. How do you convert between exponential and logarithmic forms?
2. What happens if $f(x) = 4^x$ represents a different base, such as 2 or 5?
3. What is the growth rate in this bacterial experiment?
4. How do you solve $4^x = 64$ using logarithms?
5. Can the value of $f(x)$ ever be negative in this case?

Tip: When solving exponential equations, expressing both sides with the same base simplifies the problem considerably.