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==Properties==
* A positive log-concave function is also [[Quasi-concave function|quasi-concave]].
* Every concave function that is nonnegative on its ___domain is log-concave. However, the reverse does not necessarily hold. An example is the [[Gaussian function]] {{math|''f''(''x'')}} = {{math|exp(−x<sup>2</sup>/2)}} which is log-concave since {{math|log ''f''(''x'')}} = {{math|−''x''<sup>2</sup>/2}} is a concave function of {{math|''x''}}. But {{math|''f''}} is not concave since the second derivative is positive for |{{math|''x''}}| > 1:
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* {{cite book|authorlink=Ole Barndorff-Nielsen|last=Barndorff-Nielsen|first=Ole|title=Information and exponential families in statistical theory|series=Wiley Series in Probability and Mathematical Statistics|publisher=John Wiley \& Sons, Ltd.|___location=Chichester|year=1978|pages=ix+238 pp.|isbn=0-471-99545-2|mr=489333}}
* {{cite book|title=Unimodality, convexity, and applications
|last1=Dharmadhikari|first1=Sudhakar
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