Question
Recall what you know about the change of base formula. Using the formula, write a new logarithm in 1–2 sentences so that log8256 can be easily evaluated.
Answers
GPT-4o mini
The change of base formula states that \(\log_a b = \frac{\log_c b}{\log_c a}\) for any positive number \(c\). To evaluate \(\log_8 256\) more easily, we can rewrite it using base 2:
\[
\log_8 256 = \frac{\log_2 256}{\log_2 8}.
\]
Since \(256 = 2^8\) and \(8 = 2^3\), this simplifies to:
\[
\log_8 256 = \frac{8}{3}.
\]
\[
\log_8 256 = \frac{\log_2 256}{\log_2 8}.
\]
Since \(256 = 2^8\) and \(8 = 2^3\), this simplifies to:
\[
\log_8 256 = \frac{8}{3}.
\]