I want to find the log form of this equation to simplify some of the subsequent steps. However, I am struggling with how to handle the constant, $\theta$. If anyone could explain how to log this equation, it would be much appreciated:
$$ \Pi_t^{1-\varepsilon} = \theta + (1-\theta) (P_t^{*}/P_{t-1})^{1-\varepsilon} $$
If theta were excluded, so that the equation was $\Pi_t^{1-\varepsilon} = (1-\theta) (P_t^{*}/P_{t-1})^{1-\varepsilon}$, I would understand the log form to be:
$$ (1-\varepsilon)\ln\Pi_t = \ln(1-\theta) + (1-\varepsilon)\ln(P_t^{*}/P_{t-1}) $$