Question
Recall what you know about the change of base formula. Using the formula, write a new logarithm in 1–2 sentences so that log^8 256 can be easily evaluated
Answers
GPT-4o mini
The change of base formula for logarithms states that \(\log_b a = \frac{\log_k a}{\log_k b}\) for any positive base \(k\). To evaluate \(\log_8 256\) easily, we can rewrite it using base 2, as both 8 and 256 are powers of 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:
\[
\log_8 256 = \frac{8}{3}.
\]