In the complex field, is this function Harmonic?

1. Apr 16, 2009

oab729

1. The problem statement, all variables and given/known data
Without directly verifying via the laplace equations, explain why Log|z| is harmonic in the punctured complex plane.

2. Relevant equations

3. The attempt at a solution
I thought it was because Log z is analytic on the complex plane except for the nonpositive real axis, so Log |z| would be analytic and hence harmonic since any |z| turns z into a positive real (for z=/= 0), hence Log |z| is like Log z for positive reals. But, if it's that, why would they ask to show its harmonic and not analytic.

2. Apr 17, 2009

Billy Bob

Do you have the theorem that if f=u+iv is analytic then u is harmonic?