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 base 8 256 can easily be evaluated

Answer 1

The change of base formula for logarithms allows us to express a logarithm in terms of logs with a different base: \( \log_b a = \frac{\log_k a}{\log_k b} \), where \( k \) is any positive number. To rewrite \( \log_8 256 \) for easier evaluation, we can express 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 \( \frac{8}{3} \).