To expand \( \log_{16} \) to its simplest form, we can use the change of base formula and the properties of logarithms.
The expression \( \log_{16} \) can be rewritten in terms of logarithms with base 2, since \( 16 = 2^4 \):
\[ \log_{16} x = \frac{\log_{2} x}{\log_{2} 16} \]
Calculating \( \log_{2} 16 \):
\[ \log_{2} 16 = \log_{2} (2^4) = 4 \]
Therefore,
\[ \log_{16} x = \frac{\log_{2} x}{4} \]
This implies:
\[ \log_{16} x = \frac{1}{4} \log_{2} x \]
If we multiply both sides by 4 to express it in simpler terms:
\[ 4 \log_{16} x = \log_{2} x \]
Thus, if we consider initially \( \log_{16} \) as related to \( \log_{2} \), the most direct expression that stands closest to being a correct answer in your options is:
\( 4 \log_{2} \)
So the correct response is:
4 log2