Does there exist an entire function $f(z)$ such that $e^{f(z)}= 25(e^{2z}+1)$.
Since f(z) is analytic hence $e^{f(z)}$ is analytic. Also the right hand side function is also analytic. But this doesn't guarantee the existence of such a function. I tried taking log on both sides.
$log(e^{f(z)})= log(25(e^{2z}+1))$
But here also I got stuck as log is multivalued function and I can't get $f(z)$ explicitly.
Kindly help me prove or disprove the existence of such a function.