# Sum of Logarithms

## 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 $b$.