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

= 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)