What is the answer to x^x=0.2 ?

The answer to x^x=0.2 is No Solution for x\in\mathbb{R}

The solution is No Solution for x\in\mathbb{R}

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x^x=0.2

x^{x} = 0.2

No Solution for x \in R

Solution steps

x^{x} = 0.2

Prepare

x^{x} = 0.2

for Lambert form:

x e^{- \frac{l n ( 0.2 )}{x}} = 1

Rewrite the equation with

\frac{ln ( 0.2 )}{x} = u

and

x = \frac{ln ( 0.2 )}{u}

(\frac{ln ( 0.2 )}{u}) e^{- u} = 1

Rewrite

(\frac{ln ( 0.2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = ln (0.2)

Solve

u e^{u} = ln (0.2) :

No Solution for

u \in R

No Solution for x \in R

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What is the answer to x^x=0.2 ?
The answer to x^x=0.2 is No Solution for x\in\mathbb{R}
Solve for x: x^x=0.2
The solution is No Solution for x\in\mathbb{R}