Sum of Logarithms

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Theorem

Natural Logarithm

Let $x, y \in \R$ be strictly positive real numbers.


Then:

$\ln x + \ln y = \ln \left({x y}\right)$

where $\ln$ denotes the natural logarithm.


General Logarithm

Let $x, y, b \in \R$ be strictly positive real numbers such that $b > 1$.


Then:

$\log_b x + \log_b y = \map {\log_b} {x y}$

where $\log_b$ denotes the logarithm to base $b$.


Also see


Sources