What is the answer to e^2x-4e^x-5=0 ?

The answer to e^2x-4e^x-5=0 is No Solution for x\in\mathbb{R}

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e^2x-4e^x-5=0

e^{2} x - 4 e^{x} - 5 = 0

No Solution for x \in R

Solution steps

e^{2} x - 4 e^{x} - 5 = 0

Prepare

e^{2} x - 4 e^{x} - 5 = 0

for Lambert form:

- 4 = - e^{- x} (e^{2} x - 5)

Rewrite the equation with

- x + \frac{5}{e ^{2}} = u

and

x = - \frac{e ^{2} u - 5}{e ^{2}}

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

Simplify

- 4 = e^{2} e^{\frac{e ^{2} u - 5}{e ^{2}}} u

Rewrite

- 4 = e^{2} e^{\frac{e ^{2} u - 5}{e ^{2}}} u

in Lambert form:

e^{u} u = - \frac{4}{e ^{\frac{2 e ^{2} - 5}{e ^{2}}}}

Solve

e^{u} u = - \frac{4}{e ^{\frac{2 e ^{2} - 5}{e ^{2}}}} :

No Solution for

u \in R

No Solution for x \in R

n, 4^{n + 1} = 8^{n - 2}

2^{2 x + 11} = 3^{x - 5}

(\frac{2}{5})^{x} = \frac{4}{25}

(x - 6)^{x^{2} - 5} = (x - 6)^{2 x + 3}

2^{3 x} = 8^{2 x + 1}

What is the answer to e^2x-4e^x-5=0 ?
The answer to e^2x-4e^x-5=0 is No Solution for x\in\mathbb{R}