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

Thread starter TyErd
Start date Feb 22, 2010

AI Thread Summary

To solve for x in the equations y=2/x and y=e^(x-4), the equations can be set equal to each other, leading to 2/x = e^(x-4). This simplifies to 2 = x * e^x * e^(-4). Rearranging gives the equation xe^x = 2e^4. The solution for x is expressed using the Lambert W function as x = W(2e^4), which serves as the inverse function to xe^x. The use of the Lambert W function is crucial in finding the value of x in this context.

Feb 22, 2010

TyErd

find x.

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

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Feb 22, 2010

HallsofIvy

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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.

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