Rules of Logarithms

1.	product	$\log_bxy=\log_bx+\log_by$	$\log xy=\log x+\log y$	$\ln xy=\ln x+\ln y$
2.	quotient	$\displaystyle\log_b{x\over y}=\log_bx-\log_by$	$\displaystyle\log{x\over y}=\log x-\log y$	$\displaystyle\ln{x\over y}=\ln x-\ln y$
3.	power	$\log_bx^r=r\log_bx$	$\log x^r=r\log x$	$\ln x^r=r\ln x$
4.	inverse	$\log_bb^x=x$	$\log10^x=x$	$\ln e^x=x$
5.		$b^{\log_bx}=x$	$10^{\log x}=x$	$e^{\ln x}=x$
6.		$\log_b1=0$	$\log1=0$	$\ln1=0$
7.	change of base	$\displaystyle\log_cx={{\log_bx}\over {\log_bc}}$	$\displaystyle\log_cx={{\log x}\over {\log c}}$	$\displaystyle\log_cx={{\ln x}\over {\ln c}}$
8.	log form	$x=\log_by$	$x=\log y$	$x=\ln y$
	$\Updownarrow$	$\Updownarrow$	$\Updownarrow$	$\Updownarrow$
9.	exp form	b^x=y	10^x=y	e^x=y