For $\a>0$, $0\le\b<1$, let $B_0(\alpha,\beta)$ be the class of normalised analytic functions $f$ defined in the open unit disc $D$ such that $$ \operatorname{Re}e^{i\psi}(f'(z)(f(z)/z)^{\alpha-1}-\beta)>0 $$ for $z\in D$ and for some $\psi=\psi(f)\in R$. Upper and lower bounds for the logarithmic derivative $zf'/f$ for $f\in B_0(\alpha,\beta)$ are obtained.