What is the answer to 0.8=(e^{-5+3x})/(1+e^{-5+3x)} ?

The answer to 0.8=(e^{-5+3x})/(1+e^{-5+3x)} is x=(2ln(2)+5)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

0.8=(e^{-5+3x})/(1+e^{-5+3x)}

0.8 = \frac{e ^{- 5 + 3 x}}{1 + e ^{- 5 + 3 x}}

x = \frac{2 ln ( 2 ) + 5}{3}

Decimal

x = 2.12876 \dots

Solution steps

0.8 = \frac{e ^{- 5 + 3 x}}{1 + e ^{- 5 + 3 x}}

Multiply both sides by

1 + e^{- 5 + 3 x}

0.8 (1 + e^{- 5 + 3 x}) = \frac{e ^{- 5 + 3 x}}{1 + e ^{- 5 + 3 x}} (1 + e^{- 5 + 3 x})

Simplify

0.8 (1 + e^{- 5 + 3 x}) = e^{- 5 + 3 x}

Multiply both sides by

10

8 (1 + e^{- 5 + 3 x}) = e^{- 5 + 3 x} \cdot 10

Expand

8 (1 + e^{- 5 + 3 x}) : 8 + 8 e^{- 5 + 3 x}

8 + 8 e^{- 5 + 3 x} = e^{- 5 + 3 x} \cdot 10

Move

8

to the right side

8 e^{- 5 + 3 x} = e^{- 5 + 3 x} \cdot 10 - 8

Move

e^{- 5 + 3 x} 10

to the left side

- 2 e^{- 5 + 3 x} = - 8

Divide both sides by

- 2

e^{- 5 + 3 x} = 4

Apply exponent rules

- 5 + 3 x = ln (4)

Solve

- 5 + 3 x = ln (4) : x = \frac{2 ln ( 2 ) + 5}{3}

x = \frac{2 ln ( 2 ) + 5}{3}

Verify Solutions:

x = \frac{2 ln ( 2 ) + 5}{3}

True

The solution is

x = \frac{2 ln ( 2 ) + 5}{3}

2 (3 e^{- x} x^{2} - e^{- x} x^{3}) = 0

e^{x} - 3 e^{- x} - 4 = 0

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

2 7^{x} = \frac{1}{3}

2 x - 1 216 = 6

What is the answer to 0.8=(e^{-5+3x})/(1+e^{-5+3x)} ?
The answer to 0.8=(e^{-5+3x})/(1+e^{-5+3x)} is x=(2ln(2)+5)/3