Logarithm formulas:

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

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