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Question Number 13412 by tawa tawa last updated on 19/May/17

$${\mathrm{e}}^{-\mathrm{kN}}-\mathrm{kN}-1=0$$$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{N}$$

Answered by mrW1 last updated on 20/May/17

$$e^{-kN}=kN+1$$$$e^{-kN-1}=(kN+1)e^{-1}$$$$(kN+1)e^{(kN+1)}=e$$$$kN+1=W\left(e\right)$$$$N=\frac{W\left(e\right)-1}{k}=\frac{1-1}{k}=0$$

Commented by tawa tawa last updated on 20/May/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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