en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4e^{-x}=3e^x+4

Solution

4 e^{- x} = 3 e^{x} + 4

Solution

x = ln (\frac{2}{3})

+1

Solution steps

4 e^{- x} = 3 e^{x} + 4

Apply exponent rules

4 (e^{x})^{- 1} = 3 e^{x} + 4

Rewrite the equation with

e^{x} = u

4 (u)^{- 1} = 3 u + 4

Solve

4 u^{- 1} = 3 u + 4 : u = \frac{2}{3}, u = - 2

u = \frac{2}{3}, u = - 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{2}{3} : x = ln (\frac{2}{3})

Solve

e^{x} = - 2 :

No Solution for

x \in R

x = ln (\frac{2}{3})

Popular Examples

10^x=(10^{-14})(10^2)

1 0^{x} = (1 0^{- 14}) (1 0^{2})

6(3^{2x})=2^{x+1}

6 (3^{2 x}) = 2^{x + 1}

9^{2 x - 1} = 27

ln (3) = e^{x}

e^{x} - 6 e^{- x} = 0

Frequently Asked Questions (FAQ)

What is the answer to 4e^{-x}=3e^x+4 ?
The answer to 4e^{-x}=3e^x+4 is x=ln(2/3)