What is the answer to e^2x-6e^x+5=0 ?

The answer to e^2x-6e^x+5=0 is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^2x-6e^x+5=0

e^{2} x - 6 e^{x} + 5 = 0

No Solution for x \in R

Solution steps

e^{2} x - 6 e^{x} + 5 = 0

Prepare

e^{2} x - 6 e^{x} + 5 = 0

for Lambert form:

- 6 = - 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}}

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

Simplify

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

Rewrite

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

in Lambert form:

e^{u} u = - \frac{6}{e ^{\frac{2 e ^{2} + 5}{e ^{2}}}}

Solve

e^{u} u = - \frac{6}{e ^{\frac{2 e ^{2} + 5}{e ^{2}}}} :

No Solution for

u \in R

No Solution for x \in R

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

2 5^{n - 1} + 100 = 5^{2 n - 1}

1 6^{x} = 4

4^{3 t} = 8^{t - 1}

2^{x} = 4

What is the answer to e^2x-6e^x+5=0 ?
The answer to e^2x-6e^x+5=0 is No Solution for x\in\mathbb{R}