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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!

Use the change-of-base property to rewrite the given expression in terms of natural logarithms or common logarithms. log₁₂ 16 = ?

Learn how to use the change of base property to rewrite the logarithmic expression log₁₂ 16 in terms of common or natural logarithms. This problem introduces key concepts like the change of base formula, showing equivalent expressions such as log(16)/log(12) or ln(16)/ln(12). Ideal for students in Grades 9-12.

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