I got a question about logarithm
$\log(A)+\log(B)=\log(AB)$
$\log(A)-\log(B)=\log\frac{A}{B}$
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.
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https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/properties-of-logarithms/a/justifying-the-logarithm-properties – Matti P. Jan 29 '19 at 11:21
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@JasonBourne do you understand the rules for exponential expressions? – user376343 Jan 29 '19 at 11:26
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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.
Gibbs
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