Load resistance in voltage regulator
A typical 300mW Zener uses a test current Izt=5mA with an incremental resistance Zzt and a threshold current, at 1/10 Izt or It @ 0.5mA which results in a knee resistance of Zzk approx. 10x Zzt.

The same is true for LEDs. 

Make a Thevenin equivalent circuit for 5mA at a low power.
This gives the low rated resistance, Zzt and is important to include in the equation to solve for R1.







simulate this circuit &ndash; Schematic created using CircuitLab

Now you can easily solve for R1