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Popular >

(400)/(1+e^{-x)}=350

Solution

\frac{400}{1 + e ^{- x}} = 350

Solution

x = ln (7)

+1

Decimal Notation

x = 1.94591 \dots

Solution steps

\frac{400}{1 + e ^{- x}} = 350

Multiply both sides by

1 + e^{- x}

\frac{400}{1 + e ^{- x}} (1 + e^{- x}) = 350 (1 + e^{- x})

Simplify

400 = 350 (1 + e^{- x})

Switch sides

350 (1 + e^{- x}) = 400

Divide both sides by

350

1 + e^{- x} = \frac{8}{7}

Move

1

to the right side

e^{- x} = \frac{1}{7}

Apply exponent rules

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

Solve

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

x = ln (7)

Verify Solutions:

x = ln (7)

True

The solution is

x = ln (7)

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Frequently Asked Questions (FAQ)

What is the answer to (400)/(1+e^{-x)}=350 ?
The answer to (400)/(1+e^{-x)}=350 is x=ln(7)