matemática : Logaritmos

	$\log_{a} b = x \Leftrightarrow b = a^{x}$	ex : $3^{x} = 15 \Leftrightarrow x = \log_{3} 15$
	$\log_{a} 1 = 0$	ex : $\log_{3} 1 = 0$
	$\log_{a} a = 1$	ex : $\log 10 = 1$
	$\log_{a} a^{b} = b$	ex : ${\ln e}^{2} = 2$
	$\log_{a} (u \times v) = \log_{a} u + \log_{a} v$	ex : $\log_{6} 10 + \log_{6} 2 = \log_{6} (10 \times 2) = \log_{6} 20$
	$\log_{a} (\frac{u}{v}) = \log_{a} u - \log_{a} v$	ex : $\log_{4} 9 - \log_{4} 3 = \log_{4} (\frac{9}{3}) = \log_{4} 3$
	$\log_{a} u^{v} = v \times \log_{a} u$	ex : $\log_{4} 36 = \log_{4} 6^{2} = 2 \times \log_{4} 6$
	$\log_{a} u = \frac{\log_{b} u}{\log_{b} a}$	ex : $\log_{4} 5 \times \log_{5} 6 = \log_{4} 5 \times \frac{\log_{4} 6}{\log_{4} 5} = \log_{4} 6$

matemática