Math formulas: Logarithm formulas

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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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