How do you solve a problem that has a divided variable as a base of a logarithm? My problem is Loga(x)/Log a/b(x). I guess that would be read; Log 'a' of x divided by Log 'a/b' of x. Thanks
In loga(x), which one is base? a or x? If a is the base, use change of base rule. You can take any base. So the problem becomes
Loga(x)/Log a/b(x) = [log(x)/log(a)]/[log(x)/log(a/b)] = log(a/b)/log(a) = [log(a) - log(b)]/log(a) = 1 - log(b)/log(a) = 1 - loga(b) i.e 1 - log b to the base a.