xx=Range[2,6];
yy={6.3,3.75,2.9,2.48,2.22};
dat=Transpose[{xx,yy}]

ListPlot[dat]

ListLinePlot[dat]

lsg=FindFit[dat,Log[x m,e]+s,{m,e,s},x]

yy=Log[x m,e]+s/.lsg

Plot[yy,{x,2,6},Epilog->{PointSize[.02],Red,Point/@dat}]