What is the answer to (75)/(1+15e^{-0.4x)}=25 ?

The answer to (75)/(1+15e^{-0.4x)}=25 is x=-(ln(2/15))/(0.4)

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(75)/(1+15e^{-0.4x)}=25

\frac{75}{1 + 15 e ^{- 0.4 x}} = 25

x = - \frac{ln ( \frac{2}{15} )}{0.4}

Decimal

x = 5.03725 \dots

Solution steps

\frac{75}{1 + 15 e ^{- 0.4 x}} = 25

Multiply both sides by

1 + 15 e^{- 0.4 x}

\frac{75}{1 + 15 e ^{- 0.4 x}} (1 + 15 e^{- 0.4 x}) = 25 (1 + 15 e^{- 0.4 x})

Simplify

75 = 25 (1 + 15 e^{- 0.4 x})

Switch sides

25 (1 + 15 e^{- 0.4 x}) = 75

Divide both sides by

25

1 + 15 e^{- 0.4 x} = 3

Move

1

to the right side

15 e^{- 0.4 x} = 2

Divide both sides by

15

e^{- 0.4 x} = \frac{2}{15}

Apply exponent rules

- 0.4 x = ln (\frac{2}{15})

Solve

- 0.4 x = ln (\frac{2}{15}) : x = - \frac{ln ( \frac{2}{15} )}{0.4}

x = - \frac{ln ( \frac{2}{15} )}{0.4}

Verify Solutions:

x = - \frac{ln ( \frac{2}{15} )}{0.4}

True

The solution is

x = - \frac{ln ( \frac{2}{15} )}{0.4}

7^{x^{2}} = (\frac{1}{49})^{3 x + 4}

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

e^{x^{2}} = e^{9}

e^{1 - 4 x} = 15

a^{x + 1} - a^{x} = 1

What is the answer to (75)/(1+15e^{-0.4x)}=25 ?
The answer to (75)/(1+15e^{-0.4x)}=25 is x=-(ln(2/15))/(0.4)