Question
Identify the expression equivalent to
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
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
Answers
GPT-4o mini
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 \( \log_{16} 128 \)).
\[
\frac{\log_a b}{\log_a c} = \log_c b
\]
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 \( \log_{16} 128 \)).