# $\log_{2}{3} > \log_{3}{5}$?

Which one is larger $\log_{2}{3}$ or $\log_{3}{5}$?

Edit : Without use of numerical calculations, just use properties of logarithm, exponentials. we cant use $\log 3 = 0.477$ and $\log 2 = 0. 301$ , I have already tried changing of basis and all other simple tricks with log to no avail

On the same note is there a notation for when a relation is what is sought after?

for example is there a way to write the same relation as

$$\log_{2}{3} \overset{?}{\bigcirc} \log_{3}{5}$$

where $\bigcirc$ can be one of $\le,\ge,=,<,>$

The following chain of inequalities shows that $\log_23>\log_35$: $$2\log_23=\log_23^2=\log_29>\log_28=3=\log_327>\log_325=\log_35^2=2\log_35$$