Recall what you know about the change of base formula. Using the formula, write a new logarithm in 1–2 sentences so that log8 256

Question

can be easily evaluated.

Answer 1

The change of base formula states that \(\log_b a = \frac{\log_k a}{\log_k b}\) for any positive base \(k\). To make evaluating \(\log_8 256\) easier, we can write it as \(\log_8 256 = \frac{\log_2 256}{\log_2 8}\) since both \(256\) and \(8\) are powers of \(2\).