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

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

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

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

x = ln (7)

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)

3^{2 x - 1} = 5^{x + 1}

9^{x + 3} = 2 7^{x - 1}

- 2 \cdot (- 2)^{n - 1} = (- 2)^{n}

(5^{x - 3}) (3^{2 x - 8}) = 225

2 = a^{x}

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