# random methods shit

## Index laws

$a^m \times a^n = a^{m+n}$  
$a^m \div a^n = a^{m-n}4$  
$(a^m)^n = a^{_mn}$  
$(ab)^m = a^m b^m$  
${({a \over b})}^m = {a^m \over b^m}$

## Fractional indices

$^n\sqrt{x}=x^{1/n}$

## Logarithms

$$\log_b (x) = n \quad \operatorname{where} \hspace{0.5em} b^n=x$$

## Using logs to solve index eq's

Used for equations without common base exponent

Or change base:  
$$\log_b c = {{\log_a c} \over {\log_a b}}$$

If $a<1, \quad \log_{b} a < 0$ (flip inequality operator)