Plotting – Tracing the existing curve with star symbol

b1 = {1.8743,1.8784,1.88248,1.89049,1.89828,1.90587,1.91327,1.96335,2.03035,2.12536,2.23701,2.30098,2.34255,2.37175,2.3934,2.42334,2.44307,2.48725,2.51208,2.5173,2.52799,2.53164,2.53348,2.53533 2,53625,2,53745,2,53793,2,53894,2,53909,2,53543};
ks1 = {0.01, 1, 2, 4, 6, 8, 10, 25, 50, 100, 200, 300, 400, 500, 600, 800, 1000, 2000, 4000, 5000, 10000, 15000, 20000, 30,000, 40,000, 70,000, 100,000, 1 * 10 ^ 6,1. * 10 ^ 8,1. * 10 ^ 12};
data1 = Transpose[{ks1, b1}];
s1 = ListLogLinearPlot[data1, Joined -> True, 
  PlotStyle -> {Black, Thickness[0.01]}, AxesStyle -> Black,
PlotRange -> All]

How do you put a star symbol on the same drawing that follows the curve? I know we can do this with the plot marker, but I want the track to be tracked equally from start to finish. With my data points, I do not get the tracking right. How do you achieve this?