The given equation is:

$\left(\frac{1}{6}\right)^{-2} = 36$

To convert an exponential equation to its logarithmic form, recall the general rule:

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

Here:

• Base $a = \frac{1}{6}$,
• Exponent $b = -2$,
• Result $c = 36$.

Thus, the logarithmic form of the equation is:

$\log_{\frac{1}{6}}(36) = -2$

Let me know if you want more details or clarifications!

Related Questions:

1. How do you evaluate logarithms with fractional bases like $\log_{\frac{1}{6}}(36)$?
2. What happens when you change the base of a logarithm?
3. How does the negative exponent property work with fractions?
4. What is the relationship between exponential and logarithmic functions?
5. Can you graph $\log_{\frac{1}{6}}(x)$ and explain its behavior?

Tip:

When solving logarithmic problems, always double-check that the base is positive and not equal to 1, as these are the conditions for logarithms to be valid!