Indeed, sorry for the confusion. If what you want is to change the lowest exponent shown on the axis, try SetLimits:
{
auto c1 = new TCanvas("c1","c1",1500,500);
c1->Divide(3,1);
auto hcol1 = new TH2F("hcol1","Original",40,-4,4,40,0,700);
float px, py;
for (Int_t i = 0; i < 50000; i++) {
gRandom->Rannor(px,py);
hcol1->Fill(px,100*py);
}
c1->cd(1);
hcol1->DrawCopy("COLZ");
c1->cd(2);
gPad->SetLogy(1);
hcol1->SetTitle("Logy");
hcol1->DrawCopy("COLZ");
c1->cd(3);
gPad->SetLogy(1);
hcol1->SetTitle("Logy + SetLimits");
hcol1->GetYaxis()->SetLimits(1e-1,500);
hcol1->DrawCopy("COLZ");
}
Edit: Note, by the way, that SetLimits may not be the best option, as it can alter your histogram (see this).