Series Diode Circuit Solution (Sedra Smith Exercise 3 4 f)

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This is a critical solution of series diode circuit Exercise 3.4 (f) from Sedra Smith book. Problems of Sedra Smith book is a bit difficult. This type of logic diode related problems are very important. This will help viewers to understand & solve critical logic diode related problems easily.
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Design the following circuit to provide an output voltage of 2.4v. assume that the diodes available have 0.7v drop at 1ma and that ∆v=0.1V/decade change in current.

(Sedra & Smith_exercise D4.11)
Please please solve this problem. I can't understand the conversion of decade. Please someone explain in mathematical form.

jamilajamila