logarithmic functions and rules

Question

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.

Answer 1

You need to know the definition of logarithm and some basic algebra to understand those properties.

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 $\log AB = m+n = \log A+\log B$.

Try the second one using the same ideas.