To find an equivalent expression for \( \log_2 16 \), we can first calculate \( \log_2 16 \).
Since \( 16 = 2^4 \), we have:
\[ \log_2 16 = \log_2 (2^4) = 4 \]
Now we need to evaluate the options provided:
-
Option #1: \( 3 \log 6 \)
This does not equate to \( 4 \) because \( \log 6 \) (which is in base 10 or base e, commonly) is not equal to \( \frac{4}{3} \). -
Option #2: \( \log 6 \cdot \log 6 \cdot \log 6 \)
This is \( (\log 6)^3 \), which is not equal to \( 4 \) as it is a product of logarithms. -
Option #3: \( 36 \log 6 \)
Again, this does not equate to \( 4 \) as \( 36 \log 6 \) is also a scalar multiple of \( \log 6 \).
Since none of the provided options give an expression equivalent to \( \log_2 16 = 4 \), we can conclude that none of the options are correct.
Therefore, the answer is None. None of the options provided is equivalent to \( \log_2 16 \).