α0=0.1184; μ0=91.1876; Nc=3; NF=5; M=4.4;
μmin=3; μmax=100;
β1[nf_]=(2nf-11Nc)/6; β2[nf_]=-51/4+19/12*nf;
f[μ_]=Piecewise[{{α0/(1-β1[NF-1]/2*(α0/Pi)*Log[μ^2/μ0^2]-β2[NF-1]/2*(α0/Pi)^2*Log[μ^2/μ0^2]),μ<=M},{0,μ>M}}];
c1[μ_]=2*f[M]*Log[μ/M]/(6Pi-f[M]*Log[μ/M]*(2NF-11Nc));
g[μ_]=Piecewise[{{α0/(1-β1[NF-1]/2*(α0/Pi)*Log[μ^2/μ0^2]-β2[NF-1]/2*(α0/Pi)^2*Log[μ^2/μ0^2])*(1+c1[μ]/Pi*α0/(1-β1[NF-1]/2*(α0/Pi)*Log[μ^2/μ0^2]-β2[NF-1]/2*(α0/Pi)^2*Log[μ^2/μ0^2])),μ>=M},{0,μ<M}}];
LogLinearPlot[{f[μ],g[μ]},{μ,μmin,μmax}, AxesOrigin->{μmin,0.11}, AxesLabel->{"μ (GeV)",Subscript[α,s]}, PlotRange->{f[μmin]+0.002,0.11}]