What is the answer to e^{2x}-x^3=0 ?

The answer to e^{2x}-x^3=0 is No Solution for x\in\mathbb{R}

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e^{2x}-x^3=0

e^{2 x} - x^{3} = 0

No Solution for x \in R

Solution steps

e^{2 x} - x^{3} = 0

Prepare

e^{2 x} - x^{3} = 0

for Lambert form:

1 = x e^{- \frac{2 x}{3}}

Rewrite the equation with

- \frac{2 x}{3} = u

and

x = - \frac{3 u}{2}

1 = (- \frac{3 u}{2}) e^{u}

Rewrite

1 = (- \frac{3 u}{2}) e^{u}

in Lambert form:

e^{u} u = - \frac{2}{3}

Solve

e^{u} u = - \frac{2}{3} :

No Solution for

u \in R

No Solution for x \in R

(\frac{1}{2})^{(x - 2)} + 1 = 0

3 6^{x + 1} = 6^{x^{2} + 6 x - 10}

- 4 = e^{x}

e^{2 x} + 9 e^{- 2 x} - 10 = 0

x, e^{x} - y^{2} = 0

What is the answer to e^{2x}-x^3=0 ?
The answer to e^{2x}-x^3=0 is No Solution for x\in\mathbb{R}