The problem asks to rewrite the expression $\log_{12} 16$ using the change-of-base formula.

The change-of-base formula states that: $\log_b a = \frac{\log_c a}{\log_c b}$ where $b$ is the base, $a$ is the argument, and $c$ can be any base (usually common logarithms $\log_{10}$, or natural logarithms $\ln$).

To rewrite $\log_{12} 16$, you can use either common logarithms or natural logarithms.

1. Using common logarithms ($\log_{10}$): $\log_{12} 16 = \frac{\log 16}{\log 12}$

2. Using natural logarithms ($\ln$): $\log_{12} 16 = \frac{\ln 16}{\ln 12}$

These are equivalent expressions in terms of common or natural logarithms.

Would you like further details or have any questions?

Here are five related questions to consider:

1. How do you calculate $\log_{10} 16$ and $\log_{10} 12$ using a calculator?
2. Why does the change-of-base formula work for any base?
3. What is the difference between common logarithms and natural logarithms?
4. How can you evaluate the logarithmic expression $\log_{12} 16$ to a decimal value?
5. In what scenarios would you use the change-of-base formula in real-world applications?

Tip: Use your calculator’s $\log$ or $\ln$ button to compute these values directly for faster evaluations!