Question
log
8
128
1
evaluate
8
128
1
evaluate
Answers
GPT-4o mini
To evaluate \(\log_8 128\), we can use the change of base formula for logarithms:
\[
\log_a b = \frac{\log_c b}{\log_c a}
\]
We can use base 2 for convenience because both 8 and 128 are powers of 2.
First, let's express 8 and 128 as powers of 2:
\[
8 = 2^3
\]
\[
128 = 2^7
\]
Now we can rewrite \(\log_8 128\) as:
\[
\log_8 128 = \frac{\log_2 128}{\log_2 8}
\]
Substituting the powers of 2:
\[
\log_8 128 = \frac{\log_2 (2^7)}{\log_2 (2^3)} = \frac{7}{3}
\]
Thus, the evaluated value of \(\log_8 128\) is:
\[
\boxed{\frac{7}{3}}
\]
\[
\log_a b = \frac{\log_c b}{\log_c a}
\]
We can use base 2 for convenience because both 8 and 128 are powers of 2.
First, let's express 8 and 128 as powers of 2:
\[
8 = 2^3
\]
\[
128 = 2^7
\]
Now we can rewrite \(\log_8 128\) as:
\[
\log_8 128 = \frac{\log_2 128}{\log_2 8}
\]
Substituting the powers of 2:
\[
\log_8 128 = \frac{\log_2 (2^7)}{\log_2 (2^3)} = \frac{7}{3}
\]
Thus, the evaluated value of \(\log_8 128\) is:
\[
\boxed{\frac{7}{3}}
\]