What is the answer to 0.5=(e^{-7+3x})/(1+e^{-7+3x)} ?

The answer to 0.5=(e^{-7+3x})/(1+e^{-7+3x)} is x= 7/3

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0.5=(e^{-7+3x})/(1+e^{-7+3x)}

0.5 = \frac{e ^{- 7 + 3 x}}{1 + e ^{- 7 + 3 x}}

x = \frac{7}{3}

Decimal Notation

x = 2.33333 \dots

Solution steps

0.5 = \frac{e ^{- 7 + 3 x}}{1 + e ^{- 7 + 3 x}}

Multiply both sides by

1 + e^{- 7 + 3 x}

0.5 (1 + e^{- 7 + 3 x}) = \frac{e ^{- 7 + 3 x}}{1 + e ^{- 7 + 3 x}} (1 + e^{- 7 + 3 x})

Simplify

0.5 (1 + e^{- 7 + 3 x}) = e^{- 7 + 3 x}

Multiply both sides by

10

5 (1 + e^{- 7 + 3 x}) = e^{- 7 + 3 x} \cdot 10

Expand

5 (1 + e^{- 7 + 3 x}) : 5 + 5 e^{- 7 + 3 x}

5 + 5 e^{- 7 + 3 x} = e^{- 7 + 3 x} \cdot 10

Move

5

to the right side

5 e^{- 7 + 3 x} = e^{- 7 + 3 x} \cdot 10 - 5

Move

e^{- 7 + 3 x} 10

to the left side

- 5 e^{- 7 + 3 x} = - 5

Divide both sides by

- 5

e^{- 7 + 3 x} = 1

Apply exponent rules

- 7 + 3 x = ln (1)

Solve

- 7 + 3 x = ln (1) : x = \frac{7}{3}

x = \frac{7}{3}

Verify Solutions:

x = \frac{7}{3}

True

The solution is

x = \frac{7}{3}

x e^{x} = e^{x - 1}

5^{a} = 5

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

(- 1)^{x} = 1

121 \times 1 1^{x - 2} = 3 \times 1 1^{x} - 22

What is the answer to 0.5=(e^{-7+3x})/(1+e^{-7+3x)} ?
The answer to 0.5=(e^{-7+3x})/(1+e^{-7+3x)} is x= 7/3