What is the answer to x^x= 1/2 ?

The answer to x^x= 1/2 is No Solution for x\in\mathbb{R}

Solve for x: x^x= 1/2

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

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x^{x} = \frac{1}{2}

No Solution for x \in R

Solution steps

x^{x} = \frac{1}{2}

Prepare

x^{x} = \frac{1}{2}

for Lambert form:

x e^{\frac{l n ( 2 )}{x}} = 1

Rewrite the equation with

- \frac{ln ( 2 )}{x} = u

and

x = - \frac{ln ( 2 )}{u}

(- \frac{ln ( 2 )}{u}) e^{- u} = 1

Rewrite

(- \frac{ln ( 2 )}{u}) e^{- u} = 1

in Lambert form:

u e^{u} = - ln (2)

Solve

u e^{u} = - ln (2) :

No Solution for

u \in R

No Solution for x \in R

7 e^{2 x + 3} = 20

4^{x} - 3 \cdot 2^{x + 2} + 32 = 0

27 = 3^{x + 1}

9^{1 - 7 x} = 24 3^{x - 11}

e^{x^{2}} = e^{2 x}

What is the answer to x^x= 1/2 ?
The answer to x^x= 1/2 is No Solution for x\in\mathbb{R}
Solve for x: x^x= 1/2
The solution is No Solution for x\in\mathbb{R}