Let's break down the problem in the image and find which option is equivalent to $\log 216$.

We can start by simplifying $\log 216$. Notice that 216 can be factored as: $216 = 6^3$ Thus, we can use the logarithmic property: $\log a^b = b \log a$ Applying this to $\log 216$: $\log 216 = \log (6^3) = 3 \log 6$ This means the expression that is equivalent to $\log 216$ is $3 \log 6$.

Answer:

Option #1: $3 \log 6$ is equivalent to $\log 216$.

Would you like more details or further explanations on any part of this solution? Here are five related questions for further exploration:

1. What are the key logarithmic properties used in simplifying logarithmic expressions?
2. How can you expand or condense a logarithmic expression involving products or powers?
3. Can you simplify $\log(2 \cdot 3)$ using logarithmic rules?
4. What is the logarithmic equivalent of a cube root, such as $\log \sqrt[3]{8}$?
5. How would you approach solving $\log_b (x^2) = 5$?

Tip: Remember that one of the most important logarithmic properties is the power rule: $\log_b (x^n) = n \log_b x$. It can simplify many expressions quickly!