Comparing Logs

It is hard to compare these 2 numbers directly. However, we can easily show that

$\log_2 3 > \frac{3}{2} > \log_3 5 .$

This follows because $3^2 = 9 > 8 = 2^3$ and $3^3 = 27 > 25 = 5^2$ .

Note: This is one of the "coffin problems".