Question

Which of the following is equivalent to log216
?

Option #1: 3 log6


Option #2: log6⋅log6⋅log6


Option #3: 36 log6


(1 point)
Option #

Answer 1

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:

1. **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 \( \frac{4}{3} \).

2. **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.

3. **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 \( \log_2 16 \).