Logarithm formulas:

\[ y = \log_a x \Longleftrightarrow a^y = x ~~(a, x >0 , a \ne 1)\] \[ \log_a 1 = 0\] \[ \log_a a = 1\] \[ \log_a (mn) = \log_a m + \log_a n\] \[ \log_a \frac{m}{n} = \log_a m - \log_a n\] \[ \log_a m^n = n \cdot \log_a m\] \[ \log_a m = \log_b m \cdot \log_a b\] \[ \log_a m = \frac{\log_b m}{\log_b a}\] \[ \log_a b = \frac{a}{\log_b a}\] \[ \log_a x = \frac{\ln a}{ \ln x} \]