$$$\log_{a}{1} = 0$$$ $$$\log_{a}{xy} = \log_{a}{x}+\log_{a}{y}$$$ $$$\log_{a}{b}^{c} = c \log_{a}{b}$$$ $$${b}^{\log_{b}{x}} = x$$$ $$${x}^{\log_{b}{y}} = {y}^{\log_{b}{x}} $$$ $$${\log_{a}{\sqrt[n]{b}}} = \dfrac{\log_{a}{b}}{n} $$$ $$${\log_{a}{b}} = \dfrac{\log_{c}{b}}{\log_{c}{a}}$$$ $$${\log_{a}{b}}*{\log_{b}{a}}= 1$$$

$$a^m\times\ a^n=a^{m+n}$$ 

$$\frac{a^m\ \ }{a^n}\ =a^{m-n}$$  

$$\left(a^m\right)^{^n}=a^{m\times\ n}$$  

$$\left(a\times\ b\right)^m\ =a^m\times\ b^m$$

$$a^{-m}=\ \frac{1}{a^m}$$  

 $$a^{\frac{m}{n}}=\sqrt[\ n]{a^m}$$

• Logarithms can be used to quickly find the number of digits in an exponent.