To write the given equation in logarithmic form, we use the logarithmic rule:

$a^b = c \quad \text{is equivalent to} \quad \log_a(c) = b$

For the equation $4^{-2} = \frac{1}{16}$, the base is 4, the exponent is -2, and the result is $\frac{1}{16}$.

Thus, the logarithmic form is:

$\log_4\left(\frac{1}{16}\right) = -2$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you convert $2^5 = 32$ into logarithmic form?
2. What is the logarithmic form of $10^3 = 1000$?
3. How would you express $5^4 = 625$ in logarithmic form?
4. Can you convert $3^2 = 9$ into a logarithmic equation?
5. What would $8^{-1} = \frac{1}{8}$ look like in logarithmic form?

Tip: The logarithmic form helps you find the exponent needed to reach a number from a given base.