Find the value of log(a,(b)) it uses.

Question

log base(ab) [2log base(ab)(√a)-1/2log base(ab)√ab(b)]=(log base(ab) (a))^2-(log base(ab)(b))^2

 

I do not know 

Answer 1

LHS:
log_ab[log_ab(a)-log_ab( (ab)^1/4√b)]=log_ab[log_ab(a(ab)^-1/4b^-1/2)]

 

In the RHS:

(log_ab(a))²-(log_ab(b))²=(log_ab(a))-(log_ab(b))((log_ab(a))+log_ab(b))=

=log_ab(ab)*log_ab(a/b)=log_ab(a/b), since log_ab(ab)=1

So we have

log_ab[log_ab(a(ab)^-1/4b^-1/2)]=log_ab(a/b).

We can write as

log_ab[a(ab)^-1/4b^-1/2)]=a/b =log_ab[(ab)^(a/b))]

a(ab)^-1/4b^-1/2=ab^(a/b)

Next...

The question doesn't have a precise statement.

We can write as:

log_ab(a/b)=(4/3)(a/b)

But again it is not clear what we are looking for.