is it possible to simplify this more?!?!
To start with, some of that does not look correct. You are missing the antilog in one of your "log" expressions. (log7(ofWhat?)-log76)=
... to continue, search in your book about adding or subtracting logarithms of the same base. log(A) + log(B) = ? and log(A) - log(B) = ?
Persumably you mean ln(log7 x- log7 6) for some number x that you forgot. Certainly log7 x- log7 6= log7(x/6). If that is, as you appear to be saying, log7 7, then x must have been equal to 7(6)= 42.
Yes, ln(log7(42)- log7(6))= ln(log7 7)
Further, by the very definition of log, log7= 1 so what you have reduces to just ln(1)= 0. It that simple enough?
Separate names with a comma.