What is the answer to 100=(400)/(1+0.5e^{-0.1x)} ?

The answer to 100=(400)/(1+0.5e^{-0.1x)} is x=-(ln(6))/(0.1)

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100=(400)/(1+0.5e^{-0.1x)}

100 = \frac{400}{1 + 0.5 e ^{- 0.1 x}}

x = - \frac{ln ( 6 )}{0.1}

Decimal Notation

x = - 17.91759 \dots

Solution steps

100 = \frac{400}{1 + 0.5 e ^{- 0.1 x}}

Multiply both sides by

1 + 0.5 e^{- 0.1 x}

100 (1 + 0.5 e^{- 0.1 x}) = \frac{400}{1 + 0.5 e ^{- 0.1 x}} (1 + 0.5 e^{- 0.1 x})

Simplify

100 (1 + 0.5 e^{- 0.1 x}) = 400

Divide both sides by

100

1 + 0.5 e^{- 0.1 x} = 4

Move

1

to the right side

0.5 e^{- 0.1 x} = 3

Divide both sides by

0.5

e^{- 0.1 x} = 6

Apply exponent rules

- 0.1 x = ln (6)

Solve

- 0.1 x = ln (6) : x = - \frac{ln ( 6 )}{0.1}

x = - \frac{ln ( 6 )}{0.1}

Verify Solutions:

x = - \frac{ln ( 6 )}{0.1}

True

The solution is

x = - \frac{ln ( 6 )}{0.1}

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What is the answer to 100=(400)/(1+0.5e^{-0.1x)} ?
The answer to 100=(400)/(1+0.5e^{-0.1x)} is x=-(ln(6))/(0.1)