en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^x(2e^x-1)=10

Solution

e^{x} (2 e^{x} - 1) = 10

Solution

x = ln (\frac{5}{2})

+1

Decimal Notation

x = 0.91629 \dots

Solution steps

e^{x} (2 e^{x} - 1) = 10

Rewrite the equation with

e^{x} = u

u (2 u - 1) = 10

Solve

u (2 u - 1) = 10 : u = \frac{5}{2}, u = - 2

u = \frac{5}{2}, u = - 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{5}{2} : x = ln (\frac{5}{2})

Solve

e^{x} = - 2 :

No Solution for

x \in R

x = ln (\frac{5}{2})

Popular Examples

(1/36)^x=216^{x+5}

(\frac{1}{36})^{x} = 21 6^{x + 5}

2^{x + 1} = 5^{x}

3^x-3^{x-2}=A*3^x

3^{x} - 3^{x - 2} = A \cdot 3^{x}

4^{2 x + 1} = 1

5^{4 x + 2} = 37500

Frequently Asked Questions (FAQ)

What is the answer to e^x(2e^x-1)=10 ?
The answer to e^x(2e^x-1)=10 is x=ln(5/2)