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Popular >

(50)/(1+e^{-x)}=3

Solution

\frac{50}{1 + e ^{- x}} = 3

Solution

x = - ln (\frac{47}{3})

+1

Decimal Notation

x = - 2.75153 \dots

Solution steps

\frac{50}{1 + e ^{- x}} = 3

Multiply both sides by

1 + e^{- x}

\frac{50}{1 + e ^{- x}} (1 + e^{- x}) = 3 (1 + e^{- x})

Simplify

50 = 3 (1 + e^{- x})

Switch sides

3 (1 + e^{- x}) = 50

Divide both sides by

3

1 + e^{- x} = \frac{50}{3}

Move

1

to the right side

e^{- x} = \frac{47}{3}

Apply exponent rules

- x = ln (\frac{47}{3})

Solve

- x = ln (\frac{47}{3}) : x = - ln (\frac{47}{3})

x = - ln (\frac{47}{3})

Verify Solutions:

x = - ln (\frac{47}{3})

True

The solution is

x = - ln (\frac{47}{3})

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100 - 100 (\frac{1}{4})^{x} = 70

4 (5^{x}) = 10

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5^{x + 1} + 4 (5^{x}) = 45

125^{2x+5}=625^{x+4}

12 5^{2 x + 5} = 62 5^{x + 4}

81\sqrt[5]{27}=3^x

Frequently Asked Questions (FAQ)

What is the answer to (50)/(1+e^{-x)}=3 ?
The answer to (50)/(1+e^{-x)}=3 is x=-ln(47/3)