CAT Exam 2021 Slot 3 Solved Paper

We have
${\log_15 \a + \log_32 \a}/ {(\log_15 \a) (\log_32 \a)} = 4 $
We get :
$({\log \a} / {\log 15} + {\log \a }/ { \log32 }) = 4$
${ \log \a} / { \log 15 } × { \log \a } / { \log 32} = 4 $
We get $ \log \a ( \log 32 + \log 15) = 4 \log \a $
$ \log 480 = \log \a^4 $
$\a^4 = 480$
so we can say a is between 4 and 5 .