Find x: Solving Equations for x in y=2/x and y=e^(x-4)

Thread starter TyErd
Start date Feb 22, 2010

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SUMMARY

The discussion focuses on solving the equations y=2/x and y=e^(x-4) to find the value of x. The equations are set equal to each other, leading to the expression 2/x = e^(x-4). This simplifies to the equation xe^x = 2e^4, which can be solved using the Lambert W function. The solution is expressed as x = W(2e^4), where W denotes the Lambert W function, the inverse of xe^x.

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Feb 22, 2010

TyErd

find x.

y=2/x
y=e^(x-4)

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Feb 22, 2010

HallsofIvy

Science Advisor

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TyErd said:

find x.

y=2/x
y=e^(x-4)

2/x= e^(x-4)= e^x e^(-4)

2= x e^x e^(-4)

xe^x= 2e^4

x= W(2e^4) where W is Lambert's W function:
http://en.wikipedia.org/wiki/Lambert_W_function

which is defined as the inverse function to xe^x.