What is Log

1. First law If $log_{a}x=n$ than $a^{n}=x$
2. Second law $log_{A}+log_{B}=log_{(}AB)$
3. Thirde law $log_{A}-log_{B}=log_{(}{A \over B})$
4. Fourth law If "${log_{x}}^{log_{x}}={log_{x}}^{2}=n$" than "${log_{x}}={\sqrt[{2}]{n}}$"
5. Fieth law if $log_{(}x^{n})={log_{x}}^{n}=2{log_{x}}$

examples

example 1

ex1: $log_{4}4=n$ find n.

$log_{a}x=n$ $a^{n}=x$

$4^{n}=4$

n=1

example 2

ex2: $log_{4}x=2$ find x.

$log_{a}x=n$

$a^{n}=x$

$4^{2}=x$

x = 16

example 3

ex3: $log_{a}25=2$ find x.

$log_{a}x=n$

$a^{n}=x$

$a^{2}=25$

a = 5