In one of the research paper, a function $$g(x)=\log (\exp (f(x)))$$
is proved to be concave by showing that $f(x)$ is concave. They claimed that if $f(x)$ is concave then the above composition of $\exp, \log$ will result in concavity of $g(x)$. I do not understand how this is true. But I know that log-sum-exp is a convex function. Which should mean that in the above function if $f (x)$ is linear then $g(x)$ should be convex.