Identify the expression equivalent to log2 128/log2 16

Question

.(1 point)
Responses

log4 128
logarithm subscript 4 baseline 128

log2 128
logarithm subscript 2 baseline 128

log16 128
logarithm subscript 16 baseline 128

log128 16

Answer 1

To simplify the expression \(\frac{\log_2 128}{\log_2 16}\), we can use the change of base formula for logarithms, which states that \(\frac{\log_a b}{\log_a c} = \log_c b\).

Applying this to our expression:

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

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

log16 128