Logarithms / Logs Formulas and Notes
\displaystyle \log_{1}x = 0
\displaystyle \log_{x}x = 1
\displaystyle \log_{x}{y^z} = z \cdot \log{_{x}y}
\displaystyle \log_{x}x^y = y \cdot \log_{x}x = y \left( \log_{x}x \right) = y(1) = y
\displaystyle \log_{x}y + \log_{x}z = \log_{x}{yz}
\displaystyle \log_{x}{ \left( \frac{y}{z} \right)} = \log_{x}y - \log_{x}z
\displaystyle \log_{x}{y} = \frac{1}{ \log_{y}{x} }
\displaystyle \log_{x}{y} = \frac{ \log_{a}{y} }{ \log_{a}{x} }
