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The equation shown in the image is \( \log_4 64 = x \). You are asked to rewrite it in exponential form.

The general rule to convert from logarithmic to exponential form is:

\[
\log_b a = x \quad \text{is equivalent to} \quad b^x = a
\]

Here, \( b = 4 \), \( a = 64 \), and \( x \) is the unknown exponent.

Thus, the logarithmic equation \( \log_4 64 = x \) can be rewritten in exponential form as:

\[
4^x = 64
\]

Would you like to solve for \( x \) or ask any other questions?

Here are 5 related questions to expand on this concept:
1. What is the value of \( x \) in \( 4^x = 64 \)?
2. How would you solve \( \log_b a = x \) for different bases \( b \)?
3. Can you explain the relationship between logarithms and exponents in more detail?
4. How do you compute logarithms of non-perfect powers, like \( \log_4 20 \)?
5. What happens if the base \( b \) is less than 1 in logarithmic equations?

**Tip**: To switch between logarithmic and exponential form, remember that the base of the logarithm becomes the base of the exponent, and the result becomes the exponentiated value.

Discover how to rewrite the logarithmic equation log_4 64 = x in exponential form as 4^x = 64. This problem illustrates the essential process of converting from logarithmic to exponential forms, suitable for high school students in Grades 9-12.

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