Calculus problem involving differentiable function [closed]

Question: Let $f: \mathbb{R} \to \mathbb{R}$ be a twice differentiable function, and let $a$ and $b$ be real numbers s.t. $a<b$ and$$\ln \left(\frac{f(b)+f^{\prime}(b)}{f(a)+f^{\prime}(a)}\right)=b-a$$Show that there exists at least one real number $c \in(a, b)$, s.t. $f^{\prime \prime}(c)=f(c)$.

Any ideas about this question? Thanks!