The given equation is:

$\left( \frac{1}{6} \right)^{-3} = 216$

Converting to logarithmic form:

The general form of converting an exponential equation $a^b = c$ into logarithmic form is:

$\log_a c = b$

Here:

• $a = \frac{1}{6}$
• $b = -3$
• $c = 216$

Thus, the logarithmic form is:

$\log_{\frac{1}{6}} 216 = -3$

Correct Answer:

Option A: $\log_{\frac{1}{6}} 216 = -3$

Do you need a detailed explanation on logarithmic conversions? Let me know!

Related Questions:

1. How do you convert logarithmic form back into exponential form?
2. Solve $\log_5 125 = x$.
3. What is the value of $\log_2 16$?
4. If $a^x = b$, express $x$ in terms of $a$ and $b$.
5. Simplify $\log_{10} 1000$.

Tip: Always identify the base and exponent carefully when converting between exponential and logarithmic forms.