The gain of an inverting opamp stage is -[Rf (the feed back resistor) / Rin (the input resistor)]. G = Rf/Rn.
Suppose Rf=1Ω; Rin= 1meg, then gain is -0.000001
Suppose Rf=100kΩ; Rin= 100K, then gain is -1
Suppose Rf= 1meg; Rin= 10K), then gain is -100 , which means 1mV in makes -1V out.
I think you misunderstood your instructor, or he/she doesn't know what they're talking about.
What kind of logic Gate puts out 1.27V? Sounds like you have seriously overloaded that output pin. Are you trying to connect the LED anode to the pin, cathode to ground? Are you putting a resistor in-series with the LED? What logic family? What supply voltage?