Answer- Option A
If we want to compare values of 2 log functions, they need to have the same base.
Every given log value contains $a$, either in base or in argument.Hence, we can represent all values such that they have the same base $a$.
$log_ac = log_{30!}100!$
$log_ca = \frac{1}{log_ac} = \frac{1}{log_{30!}100!}$
$log_ab = log_{30!}50!$
$log_ba = \frac{1}{log_ab} = \frac{1}{log_{30!}50!}$
If $x_{1} > x_{2}$, $log_ax_{1} > log_ax_{2}$ where $a > 1$
Hence,
$ log_{30!}100! > log_{30!}50! > \frac{1}{log_{30!}50!} > \frac{1}{log_{30!}100!}$
$log_ac > log_ab > log_ba > log_ca$
This is same as option A.