## Damn you, Napier!

January 15, 2013

Briggs‘ logarithms (often mistakenly understood to be Napier‘s logarithms) is such an useful function that most of us don’t really think about it, until we have to. Everyone’s familiar with its properties:

$\displaystyle\log_b a = \frac{\log a}{\log b}$

$\log b^x = x \log b$

$\log a b = \log a + \log b$ (1)

$\displaystyle\log \frac{a}{b} = \log a - \log b$

but suddenly,

$\log (a+b) = ?$

What can we do with this last one?