Sum of Logarithms
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Theorem
Natural Logarithm
Let $x, y \in \R$ be strictly positive real numbers.
Then:
- $\ln x + \ln y = \map \ln {x y}$
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
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles: Logarithms
- For a video presentation of the contents of this page, visit the Khan Academy.