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Math formulas: Logarithm formulas

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Logarithm formulas

y=logaxay=x  (a,x>0,a1) y = \log_a x \Longleftrightarrow a^y = x ~~(a, x >0 , a \ne 1)
loga1=0 \log_a 1 = 0
logaa=1 \log_a a = 1
loga(mn)=logam+logan \log_a (mn) = \log_a m + \log_a n
logamn=logamlogan \log_a \frac{m}{n} = \log_a m - \log_a n
logamn=nlogam \log_a m^n = n \cdot \log_a m
logam=logbmlogab \log_a m = \log_b m \cdot \log_a b
logam=logbmlogba \log_a m = \frac{\log_b m}{\log_b a}
logab=alogba \log_a b = \frac{a}{\log_b a}
logax=lnalnx \log_a x = \frac{\ln a}{ \ln x}

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