# logarithmic functions and rules

I got a question about logarithm

1. $$\log(A)+\log(B)=\log(AB)$$

2. $$\log(A)-\log(B)=\log\frac{A}{B}$$

I was reading on wikipedia on it and try to understand how the rule come about, but I can't understand.

Can anyone help to understands it.

By definition if $$a > 0, a \neq 1$$ and $$N > 0$$, then $$\log_a N$$ is a number $$b$$ such that $$a^b = N$$.
About your properties: say the basis of your logarithms is $$a$$. Then $$\log A$$ is a number $$m$$ such that $$a^m = A$$, and likewise $$\log B = n$$ means $$a^n = B$$. Then $$AB = a^ma^n = a^{m+n}$$, or equivalently $$\log AB = m+n = \log A+\log B$$.