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.