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For μ ∈ ℂ such that Re μ > 0 let ${ℱ}_{\mu }$ denote the class of all non-vanishing analytic functions f in the unit disk with f(0) = 1 and $Re(2\pi /\mu z{f}^{\text{'}}\left(z\right)/f\left(z\right)+(1+z)/(1-z))>0$ in . For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ ̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class ${ℱ}_{\mu }\left(\lambda \right)=f\in {ℱ}_{\mu }:f^{\text{'}}\left(0\right)=(\mu /\pi )(\lambda -1)and{f}^{\text{'}\text{'}}\left(0\right)=(\mu /\pi )\left(a\right(1-\left|\lambda \right|²)+(\mu /\pi )(\lambda -1)²-(1-\lambda ²))$. In the final section we graphically illustrate the region of variability for several sets of parameters.