Question

Which of the following is equivalent to log216
?
only optoions i gave
\
Option #1: 3log6

Option #2: log6⋅log6⋅log6

Option #3: 36log6

(1 point)
Option #

Answer 1

To determine which of the given options is equivalent to \( \log_2 16 \), let's first simplify \( \log_2 16 \).

We know that \( 16 = 2^4 \), so:
\[
\log_2 16 = \log_2 (2^4) = 4
\]

Now, let's analyze each option to see if any of them equal 4 when evaluated.

**Option #1: \( 3\log 6 \)**

Using the change of base formula:
\[
\log_2 6 = \frac{\log 6}{\log 2}
\]
Thus:
\[
3 \log_2 6 = 3 \cdot \frac{\log 6}{\log 2}
\]
This value will not equal 4.

**Option #2: \( \log 6 \cdot \log 6 \cdot \log 6 \)**

This evaluates to:
\[
(\log 6)^3
\]
Again, this value will not equal 4.

**Option #3: \( 36 \log 6 \)**

Using the change of base formula again:
\[
36 \log_2 6 = 36 \cdot \frac{\log 6}{\log 2}
\]
This value will also not equal 4.

None of the options provided are equivalent to \( \log_2 16 \) which equals 4. Therefore, the answer is that none of the options correctly represent \( \log_2 16 \).

If you only want to choose from the options given, you would explain that none are correct, but if forced to choose one, it would likely be clear that none represent the intended value based on your original statement.