Let $h$ be a real valued harmonic function on the twice punctured plane $Ω=\Bbb C \setminus \{0, 1\}$. Show that there exist unique real numbers $a_0, a_1$ such that $$u(z)=h(z)−a_0 \log |z|−a_1 \log |z−1|$$ is the real part of a holomorphic function on $Ω$.
All I can think of is use Cauchy-Riemann equations, but I cannot go anywhere with the integral. Can someone help me?