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# 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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