Identify the expression equivalent to

Question

log
2
128
log
2
16
.(1 point)
Responses

log
4
128
logarithm subscript 4 baseline 128

log
128
16
logarithm subscript 128 baseline 16

log
2
128
logarithm subscript 2 baseline 128

log
16
128

Answer 1

To simplify the expression \( \frac{\log_2 128}{\log_2 16} \), we can use the change of base formula for logarithms:

\[ \frac{\log_a b}{\log_a c} = \log_c b \]

In this case, we can rewrite the expression as follows:

\[ \frac{\log_2 128}{\log_2 16} = \log_{16} 128 \]

So, the expression equivalent to \( \frac{\log_2 128}{\log_2 16} \) is:

logarithm subscript 16 baseline 128 (or \( \log_{16} 128 \)).