Question

Prove that log 5040 = 4 log 2 + 2 log 3+log5

Answer 1

There is something wrong in the question.
On the RHS side there should be log 7

We have to show that RHS = LHS

RHS = 4 log 2 + 2 log 3 + log 5 + log 7
= log (2)^4 + log (3)^2 + log 5 + log 7
= log ( 16 x 9 x 5 x 7)
= log 5040
= LHS

Hope This Helps You!

Answer 2

write 5040 as product of primes
5040= 2*2*2*2*3*3*5*7
=2^4*3^2*5*7
we use
log xy = log x+ log y
log a^n = n log a
now given

lhs =log 5040
= log (2^4*3^2* 5*7)
= log 2^4 + log 3^2 +log 5 + log 7
=4 log 2 + 2 log 3 + log 5 + log 7
=rhs