What is the answer to x=4^x ?

The answer to x=4^x is No Solution for x\in\mathbb{R}

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

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x=4^x

x = 4^{x}

No Solution for x \in R

Solution steps

x = 4^{x}

Prepare

x = 4^{x}

for Lambert form:

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

Rewrite the equation with

- 2 ln (2) x = u

and

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

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

Rewrite

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

in Lambert form:

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

Solve

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

No Solution for

u \in R

No Solution for x \in R

8^{x - 8} = 9

e^{x^{2}} - e^{5} e^{x - 1} = 0

11 (3 + e^{- x})^{- 1} = 2

11 (3 + e^{- x})^{- 1} = 3

8^{(x + 3)} = 32

What is the answer to x=4^x ?
The answer to x=4^x is No Solution for x\in\mathbb{R}
Solve for x: x=4^x
The solution is No Solution for x\in\mathbb{R}