Calculating resistance when ohm law has no response
LEDs are diodes and diodes do not have a constant forward voltage. The forward voltage is actually a function of current.

Behold:



This curve came from the datasheet of a white LED that is advertised at 3.1V. But you can see that it only achieves 3.1V at 60mA (at 25°C). The manufacturer of the LED will have chosen a nominal current that makes the LED as bright as possible without limiting the promised useful life. You certainly don't need to use that exact current value. A lower current will correspond to a lower forward voltage. You'll need to find the relevant plot in the datasheet for your LED.

For example, let's say the plot in your LED's datasheet shows 5mA corresponds to a 2.8V forward drop. Your calculation becomes:

Example:

$$\frac{3V - 2.8V}{5mA} = 40\Omega$$