- #1

#### Ben-CS

Problem 1:

e^-x = x

Solve for x.

Problem 2:

x^y - y^x = xy - x - y

Solve for y.

e^-x = x

Solve for x.

Problem 2:

x^y - y^x = xy - x - y

Solve for y.

Last edited by a moderator:

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- Thread starter Ben-CS
- Start date

- #1

Problem 1:

e^-x = x

Solve for x.

Problem 2:

x^y - y^x = xy - x - y

Solve for y.

e^-x = x

Solve for x.

Problem 2:

x^y - y^x = xy - x - y

Solve for y.

Last edited by a moderator:

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- #2

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The first can be solved numerically or they can be solved in terms of the "Lambert W function".

- #3

e^-x = x

e^x = 1/x

x e^x = 1

x = ProductLog(1), where ProductLog (a.k.a. Lambert's W-function) is defined as the inverse of f(W) = W e^W

Numerically, the answer is about 0.567143290409784

Problem 2:

I don't know. Sorry.

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