Answer
$\log_4{258} \gt \log_5{620}$
Work Step by Step
RECALL:
The change-of-base formula for logarithms:
$\log_b{x} = \dfrac{\log_a{x}}{\log_a{b}}$
Use the formula above and use base 10 to evaluate each of the given logarithms:
$\log_{4}{258} = \dfrac{\log{258}}{\log{4}}\approx 4.005614$
$\log_5{620} = \dfrac{\log{620}}{\log{5}} \approx 3.995009$
Thus, $\log_4{258} \gt \log_5{620}$.
