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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.

The number of bacteria in an experiment can be represented by f(x) = 4^x, where x represents the number of hours. What is x when f(x) = 64?

Learn how to solve the exponential equation 4^x = 64. This problem demonstrates key algebraic concepts such as exponential functions and properties of exponents. Ideal for students in Grades 8-10 who are learning to work with exponential growth and equations.

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