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

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

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x=3e^{2x}

x = 3 e^{2 x}

No Solution for x \in R

Solution steps

x = 3 e^{2 x}

Prepare

x = 3 e^{2 x}

for Lambert form:

x e^{- 2 x} = 3

Rewrite the equation with

- 2 x = u

and

x = - \frac{u}{2}

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

Rewrite

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

in Lambert form:

e^{u} u = - 6

Solve

e^{u} u = - 6 :

No Solution for

u \in R

No Solution for x \in R

4^{- (x - 4)} = \frac{1}{16}

a = 30 \cdot 5^{0.078 x}

3^{x + 2} - 10 \cdot 3^{x} + 9 = 0

9 e^{5 x} = 100

32 = 1 6^{x - 1}

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