Editing Logarithmically convex function (section)

==Properties==
A logarithmically convex function ''f'' is a convex function since it is the [[function composition|composite]] of the [[increasing function|increasing]] convex function <math>\exp</math> and the function <math>\log\circ f</math>, which is by definition convex.  However, being logarithmically convex is a strictly stronger property than being convex.  For example, the squaring function <math>f(x) = x^2</math> is convex, but its logarithm <math>\log f(x) = 2\log |x|</math> is not.  Therefore the squaring function is not logarithmically convex.