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I am trying to graph the following equation...

vm = 0.76;
Km = 16.7;
S0 = 100.0;
t = Range[0, 500, 1];
NSolve[(1/vm)*(S0 - Km (Log[S/S0])) - S == t, S]

But this requires me to solve for S, for every t (from [0,500]) values, then plot it. However, when I run this, NSolve does not return anything.

How can I solve for S, over a range of values, then plot it?

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Solve works

ClearAll[s,t]
vm=76/100;
Km=167/10;
S0=100;
sol=First@Solve[(1/vm)*(S0-Km (Log[s/S0]))-s==t,s]

Mathematica graphics

Plot[s/.sol,{t,0,500}]

Mathematica graphics

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