how about i just tell you this:

when one number is exponentiated by c, you multiply the exponent of the number by c, right?

a*log(b) = log(b^a)

when one number of the same base divides another, you subtract their exponents right?

log(a) - log(b) = log(a/b)

when two numbers of the same base multiply together, you add their exponents right?

log(a) + log(b) = log(a*b)