What is the answer to t=5e^{2t} ?

The answer to t=5e^{2t} is No Solution for t\in\mathbb{R}

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t=5e^{2t}

t = 5 e^{2 t}

No Solution for t \in R

Solution steps

t = 5 e^{2 t}

Prepare

t = 5 e^{2 t}

for Lambert form:

t e^{- 2 t} = 5

Rewrite the equation with

- 2 t = u

and

t = - \frac{u}{2}

(- \frac{u}{2}) e^{u} = 5

Rewrite

(- \frac{u}{2}) e^{u} = 5

in Lambert form:

e^{u} u = - 10

Solve

e^{u} u = - 10 :

No Solution for

u \in R

No Solution for t \in R

2^{(2 x + 3)} + 2^{(x + 3)} = 1 + 2^{x}

2^{n} = 1024

5^{4 x} = \frac{1}{5} 5

3^{2 x + 1} = 2^{x - 4}

x, e^{x} = - 1

What is the answer to t=5e^{2t} ?
The answer to t=5e^{2t} is No Solution for t\in\mathbb{R}