# How to analyze this diode circuit for a resistance?

I'm sorry for posting a textbook question, but it does not provide any explanation and I am pulling hair trying to make sense of this.

I tried converting each of the diodes to a 0.7V DC source with positive terminals up. Then I thought I found the equivalent resistance of the 3 diodes by

Rd = Vd/Id = (0.7 * 3 V)/(1 mA) = 2100 ohms


Then I did a voltage divider

Vo = Vin * Rd / (Rd + R)


Rearranged for R

R = Vin * Rd / Vo - Rd


Plugged in the values

R = (10 - 0.7 * 3) * 2100 / 2.4 - 2100
R = 4812.5


Which isn't even remotely close to the supplied answer of 139.

I've been at this for over an hour and I'm too stubborn to ignore it but obviously not learned enough to figure it out yet. Can you help me see what I'm missing? EDIT: Full Solution

$$I = I_s e^{\frac{v}{v_t}}$$

$$I_s = \frac{I}{e^{\frac{v}{v_t}}} = \frac{0.001}{e^{\frac{0.7}{0.025}}} \approx 6.914 \cdot 10^{-16}$$

$$I = I_s e^{\frac{v}{v_t}} = (I_s) e^{\frac{2.4 / 3}{0.025}} = 0.0546\, A$$

$$R = \frac{v}{i} = \frac{10 - 2.4}{0.0546} = 139$$