Which of the following expressions correctly expands log16

Question

to its simplest form?(1 point)
Responses

log8⋅log2
logarithm 8 times logarithm 2

4log2
4 logarithm 2

2log8
2 logarithm 8

16log1

Answer 1

To expand \( \log_{16} \) into its simplest form, we can use the change of base formula and properties of logarithms. Specifically, we can express \( \log_{16} \) in terms of \( \log_{2} \).

Since \( 16 = 2^4 \), we can write:

\[ \log_{16} = \log_{2^4} = \frac{1}{4} \log_{2} = 4 \log_{2} \]

The correct expansion of \( \log_{16} \) to its simplest form from the options given is:

4 log 2.