Logarithmic questions

What you've given that:
log_a(M) = log_a(M) / log_b(a)
is not an identity

In fact, the identity is
log_a(M) = log_b(M) / log_b(a)

Then change log_2 6 into base 10:
log_2(6)
= log_10(2) / log_10(6)
~ 0.3010 / 0.7782
= 0.3869



log_3(75) x log_5(45) - [log_3(25) + log_5(9)]
(Change all into base 3)
= log_3(75) x log_3(45)/log3_(5) - [log_3(25) + log_3(9)/log_3(5)]
= log_3(3 x 5^2) x log_3(5 x 3^2)/log3_(5) - [log_3(5^2) + log_3(3^2)/log_3(5)]
= [1 + 2log_3(5)][log_3(5) + 2]/log_3(5) - [2log_3(5) + 2/log_3(5)]
= {2[log_3(5)]^2 + 5log_3(5) + 2}/log_3(5) - 2log_3(5) - 2/log_3(5)
= 2log_3(5) + 5 + 2/log_3(5) - 2log_3(5) - 2/log_3(5)
= 5