What is the answer to roots e^{-x}-x ?

The answer to roots e^{-x}-x is x=\W_{0}(1)

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roots e^{-x}-x

roots

e^{- x} - x

x = W_{0} (1)

Solution steps

e^{- x} - x

The roots are the intercepts with the x-axis

(y = 0)

e^{- x} - x = 0

Rewrite

e^{- x} - x = 0

in Lambert form:

x e^{x} = 1

Solve

x e^{x} = 1 : x = W_{0} (1)

x = W_{0} (1)

\frac{100}{e ^{2 x}} = \frac{300}{e ^{4 x}}

5^{2 x} - 2 \times 5^{x} - 15 = 0

5^{x + 3} = 125

7^{x} = 343

e^{2 x} - 2 e^{x} - 8 = 0

What is the answer to roots e^{-x}-x ?
The answer to roots e^{-x}-x is x=\W_{0}(1)