To expand \( \log 16 \) to its simplest form, we can use the properties of logarithms.
First, note that \( 16 = 2^4 \). Therefore, we can express \( \log 16 \) as follows:
\[ \log 16 = \log(2^4) \]
Using the power rule of logarithms, which states that \( \log(a^b) = b \cdot \log(a) \), we can simplify this:
\[ \log(2^4) = 4 \cdot \log(2) \]
Now, looking at the response options:
- \( \log 8 \cdot \log 2 \) is incorrect.
- \( 2 \log 8 \) is incorrect.
- \( 4 \log 2 \) is correct.
- \( 16 \log 1 \) is incorrect (since \( \log 1 = 0 \), this results in \( 0 \)).
So, the correct expression that expands \( \log 16 \) to its simplest form is:
4 log 2.