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We are given the following equation:

\[
\left( \frac{1}{4} \right)^{-3} = 64
\]

To express this equation in logarithmic form, we first simplify the expression:

\[
\left( \frac{1}{4} \right)^{-3} = \left( \frac{4}{1} \right)^3 = 4^3 = 64
\]

Now, rewriting this as a logarithmic equation, we use the logarithmic identity:

\[
a^b = c \quad \text{can be written as} \quad \log_a(c) = b
\]

In this case, \(4^3 = 64\), so we express it as:

\[
\log_4(64) = 3
\]

This is the logarithmic form of the given equation.

Do you need further clarification or details? Here are some related questions for further exploration:

1. How would you express \((\frac{1}{9})^{-2} = 81\) in logarithmic form?
2. Can you convert \(64 = 2^6\) into its logarithmic form?
3. What happens when you have a negative exponent with a base less than 1?
4. How does changing the base affect the logarithmic equation?
5. How do you solve logarithmic equations like \(\log_4(64) = 3\)?

**Tip:** When working with logarithms, always remember the base in both exponential and logarithmic forms, as they must remain consistent.

Learn how to convert the equation (1/4)^(-3) = 64 into its logarithmic form using key concepts like exponents and logarithms. This solution is suitable for students in Grades 8-10 and explains the step-by-step process of converting exponential equations to logarithms.

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