Exponential trigonometric function zeroes

Question

How would I find the zero of this exponential function:

$f(x)= sin e^x$

After i set the equation to zero, what do i do? Does this involve finding the derivatives?

Answer 1

$$ 0 = \sin(e^x) \Rightarrow \\ k \, \pi = e^x \quad \Rightarrow \\ x = \ln(k \, \pi) $$ where $k \in \mathbb{N}$. I only considered real solutions.