Question

log4(1/64)

Answer 1

\(log_4\left(\dfrac{1}{64}\right) = log_4(64^{-1}) = log_4(4^{3(-1)}) = log_44^{-3}\)

Now express, let's do the other part using the rule: \(log_ax = \dfrac{lnx}{lna}\)

\(log_4 4^{-3} = \dfrac{ln4^{-3}}{ln4} = \dfrac{-3ln4}{ln4} = -3\)