What is the answer to (100)/(1+15e^{-0.4x)}=20 ?

The answer to (100)/(1+15e^{-0.4x)}=20 is x=-(ln(4/15))/(0.4)

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(100)/(1+15e^{-0.4x)}=20

\frac{100}{1 + 15 e ^{- 0.4 x}} = 20

x = - \frac{ln ( \frac{4}{15} )}{0.4}

Decimal Notation

x = 3.30438 \dots

Solution steps

\frac{100}{1 + 15 e ^{- 0.4 x}} = 20

Multiply both sides by

1 + 15 e^{- 0.4 x}

\frac{100}{1 + 15 e ^{- 0.4 x}} (1 + 15 e^{- 0.4 x}) = 20 (1 + 15 e^{- 0.4 x})

Simplify

100 = 20 (1 + 15 e^{- 0.4 x})

Switch sides

20 (1 + 15 e^{- 0.4 x}) = 100

Divide both sides by

20

1 + 15 e^{- 0.4 x} = 5

Move

1

to the right side

15 e^{- 0.4 x} = 4

Divide both sides by

15

e^{- 0.4 x} = \frac{4}{15}

Apply exponent rules

- 0.4 x = ln (\frac{4}{15})

Solve

- 0.4 x = ln (\frac{4}{15}) : x = - \frac{ln ( \frac{4}{15} )}{0.4}

x = - \frac{ln ( \frac{4}{15} )}{0.4}

Verify Solutions:

x = - \frac{ln ( \frac{4}{15} )}{0.4}

True

The solution is

x = - \frac{ln ( \frac{4}{15} )}{0.4}

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3^{x} - \frac{4}{3 ^{x}} = 3

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

What is the answer to (100)/(1+15e^{-0.4x)}=20 ?
The answer to (100)/(1+15e^{-0.4x)}=20 is x=-(ln(4/15))/(0.4)