Consider this function $f(x)=-x\log\log(bx)+x\log\log\log(bx)+ax$, where $a$ and $b$ are positive constants, and the logarithms are 2-based.

Is it possible to find the maximum value (or even with approximation) of $f(x)$, in terms of $a$ and $b$, for $x>\frac{16}{b}$?

Note, it can be shown that $f(x)$ is concave for $x>\frac{16}{b}$.