Logarithmically concave function

A function ${\displaystyle f}$ is log-concave, if its natural log ${\displaystyle \ln(f(x))}$, is concave. Every concave function is log-concave, however the reverse does not necessarily hold (i.e., ${\displaystyle \exp {-x^{2}})}$.

In parallel, a function is log-convex if its natural log is convex.