show that log (a/b)+ log (b/a)=0

Question

basic concept 

Answer 1

Another way to prove this:

 

log(a/b) + log(b/a) = log(a/b) + log[(a/b)^-1] = log(a/b) - log(a/b) = 0

 

Either way, you use the properties of logarithms.

Answer 2

Apply the addition property of logarithms.

 

log[(a/b)(b/a)] = 0

 

log(1) = 0

 

True statement.