Wikipedia:Reference desk/Archives/Mathematics/2011 November 9

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

November 9

Laws of Logs

What happens if a logarithm has a coefficient. What effect does this have on logarithms?

For example, how could log(a)-nlog(b) be written as a single logarithm?

Would n have to be written as a power of b?

--T.M.M. Dowd (talk) 19:52, 9 November 2011 (UTC)

Yes. $n\log(b)=\log(b^{n})\,\!$, so $\log(a)-n\log(b)=\log \left({\frac {a}{b^{n}}}\right)$. -- Meni Rosenfeld (talk) 20:11, 9 November 2011 (UTC)