Is there some reason why you insist upon posting attachments after you have been told its a bad idea?
It's not all that difficult to type:
(this would look much nicer in LaTex but I have typed it in ASCII)
z= |z|e^(i theta)
ln z= ln |z| e^(i theta) (Well, ln z= ln(z e^(i theta)) is correct)
ln z= ln |z|+ ln(e^i theta)
ln z= ln |z|+ i ln(theta)
i.e. log(z)= ln z
Assuming that your textbook has specified a convention that natural logarithm applied to complex numbers will be designated by "log", which is implied by the question itself, then it is not correct to write "ln z". Other than that, what you wrote is correct.