#### Answer

$\log_{4}258\gt \log_{5}620$

#### Work Step by Step

We find a number near $258$ that it is easier to take $\log_{4}$ of:
$\log_{4}258\gt \log_{4}256$
$\log_{4}258\gt \log_{4}4^{4}$
$\log_{4}258\gt 4$
Next, we find a number near $620$ that it is easier to take $\log_{5}$ of:
$\log_{5}620\lt \log_{5}625$
$\log_{5}620\lt \log_{5}5^{4}$
$\log_{5}620\lt 4$
Therefore:
$\log_{4}258\gt \log_{5}620$