Is log 5 equivalent to log 5-log 20?
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.