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Popular >

(50)/(1+e^{-x)}=4

Solution

\frac{50}{1 + e ^{- x}} = 4

Solution

x = - ln (\frac{23}{2})

+1

Decimal Notation

x = - 2.44234 \dots

Solution steps

\frac{50}{1 + e ^{- x}} = 4

Multiply both sides by

1 + e^{- x}

\frac{50}{1 + e ^{- x}} (1 + e^{- x}) = 4 (1 + e^{- x})

Simplify

50 = 4 (1 + e^{- x})

Switch sides

4 (1 + e^{- x}) = 50

Divide both sides by

4

1 + e^{- x} = \frac{25}{2}

Move

1

to the right side

e^{- x} = \frac{23}{2}

Apply exponent rules

- x = ln (\frac{23}{2})

Solve

- x = ln (\frac{23}{2}) : x = - ln (\frac{23}{2})

x = - ln (\frac{23}{2})

Verify Solutions:

x = - ln (\frac{23}{2})

True

The solution is

x = - ln (\frac{23}{2})

Popular Examples

4^{x^2+4x}=2^{-6}

4^{x^{2} + 4 x} = 2^{- 6}

81^{x-3}=(1/9)^{2x-1}

8 1^{x - 3} = (\frac{1}{9})^{2 x - 1}

\frac{1}{25} = 5^{x + 4}

7^{x - 10} = 25

8^{(x^2+2x-15)}=1

8^{(x^{2} + 2 x - 15)} = 1

Frequently Asked Questions (FAQ)

What is the answer to (50)/(1+e^{-x)}=4 ?
The answer to (50)/(1+e^{-x)}=4 is x=-ln(23/2)