What is the Iout calculation for a BJT circuit with infinite gain?

[etf]

Hi!
Here is my task:
Calculate Iout if all BJT's have identical characteristics with β→∞, work on same temperature in forward active mode. Use BJT exponential transfer characteristic.

Since β→∞, IB for every BJT should be zero amps and IC=IE. Equation for BJT exponential transfer characteristic is Ic=Is*e^(VBE/Vt) but I don't know how to use it in order to find Iout. Any idea? Iout should be I1*I2/I3.

 

[rude man]

Using ic1 = is exp(Vbe1/VT), compute Vbe1. Note ic1 = I1.
Then using I2, compute Vbe2.
Etc. until you get to Vbe4. Finally, compute ic4 = Iout.

 

[etf]

Done. Thanks a lot!