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.