Logarithm

A logarithm is a shorthand way of expressing exponentional notation.

Introductory

The general form for a logarithm can be expressed as $\log_x y=z$ which means $x^z=y$ . We would read this as "The logarithm of y base x is z". We have $3^3=27$ . To express this in Logarithmic notation, we would write it as $\log_3 27=3$ . When a logarithm has no base, it is assumed to be base 10.

Logarithmic Properties

These hold for all logarithms.

$\log_a b^n=n\log_a b$
$log_a b+ \log_a c=\log_a bc$
$\log_a b-\log_a c=\log_a \frac{b}{c}$
$(\log_a b)(\log_c d)= (\log_a d)(\log_c b)$
$\frac{\log_a b}{\log_a c}=\log_c b$
$\log_a^n b^n=\log_a b$

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Logarithm

Introductory

Logarithmic Properties