Is log 5 equivalent to log 5-log 20?

Answer 1

No. log 20 is a positive number , so it you subtract it from log 5 you get less than log 5.

However, log10 5 = 1 - log102 = 2- log1020 .

or

log 5 - log 20 = log 5 - log 4*5 = log 5 - (log 5 + log 4) = log 5 - log 5 - log 4 = - log 4

But we do not need to do all of these computations, because log 5 is different from log 5 - log 20 by the law of the equality that says two equals remain equal if and only if we subtract (in our case) the same thing from them.