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.

Answer 1

The change of base formula for logarithms states that \(\log_b a = \frac{\log_k a}{\log_k b}\) for any positive \(k\). To rewrite \(\log_{8} 256\) using base 2, we can express it as \(\log_{8} 256 = \frac{\log_{2} 256}{\log_{2} 8}\). Since \(256 = 2^8\) and \(8 = 2^3\), this becomes \(\log_{8} 256 = \frac{8}{3}\), making it easier to evaluate.