More Complex Analysis-Removable Singularity

[WannaBe22]

Homework Statement

Let f be analytic in the region $$(z:0<|z-a|<r)$$ and isn't defined at $$z=a$$.
Prove that if there is a neighborhood of z=a where $$Re f(z)>0$$ then z=a is a removable singularity of f.


Hope you'll be able to help me
Thanks in advance

Homework Equations

The Attempt at a Solution

 

[Count Iblis]

Hint: Consider Log[f(z)].

 

[WannaBe22]

thanks!