To express the equation \( 4^{-2} = \frac{1}{16} \) in logarithmic form, follow these steps:

1. Recognize that the equation \( 4^{-2} = \frac{1}{16} \) can be rewritten as:
   \[
   4^{-2} = \left(\frac{1}{16}\right)
   \]

2. Recall that the logarithmic form is the inverse of the exponential form. The general form for an exponential equation \( b^x = y \) is converted to logarithmic form as:
   \[
   \log_b(y) = x
   \]
   Where:
   - \( b \) is the base of the exponent (here \( b = 4 \)).
   - \( y \) is the result of the exponentiation (here \( y = \frac{1}{16} \)).
   - \( x \) is the exponent (here \( x = -2 \)).

3. Applying this to your equation:
   \[
   4^{-2} = \frac{1}{16}
   \]
   The corresponding logarithmic form is:
   \[
   \log_4\left(\frac{1}{16}\right) = -2
   \]

So, the logarithmic equation is:
\[
\log_4\left(\frac{1}{16}\right) = -2
\]

Would you like more details on this or have any further questions?

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Here are some related questions:
1. How do you convert a logarithmic equation back into an exponential equation?
2. What is the logarithmic form of \( 2^3 = 8 \)?
3. How can you solve logarithmic equations involving different bases?
4. What does the value of a negative logarithm represent?
5. How would the equation change if the base was a different number?

**Tip:** When dealing with logarithms, remember that a negative exponent means the reciprocal of the base raised to the positive exponent.

Understand how to convert 4^-2 = 1/16 into a logarithmic equation. This problem covers exponential equations and logarithmic forms, explaining the relationship between these concepts. Suitable for students in Grades 10-12.

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