What is the answer to (15)/(1+2e^{-0.5n)}=7.5 ?

The answer to (15)/(1+2e^{-0.5n)}=7.5 is n=(ln(2))/(0.5)

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(15)/(1+2e^{-0.5n)}=7.5

\frac{15}{1 + 2 e ^{- 0.5 n}} = 7.5

n = \frac{ln ( 2 )}{0.5}

Decimal Notation

n = 1.38629 \dots

Solution steps

\frac{15}{1 + 2 e ^{- 0.5 n}} = 7.5

Multiply both sides by

1 + 2 e^{- 0.5 n}

\frac{15}{1 + 2 e ^{- 0.5 n}} (1 + 2 e^{- 0.5 n}) = 7.5 (1 + 2 e^{- 0.5 n})

Simplify

15 = 7.5 (1 + 2 e^{- 0.5 n})

Switch sides

7.5 (1 + 2 e^{- 0.5 n}) = 15

Divide both sides by

7.5

1 + 2 e^{- 0.5 n} = 2

Move

1

to the right side

2 e^{- 0.5 n} = 1

Divide both sides by

2

e^{- 0.5 n} = \frac{1}{2}

Apply exponent rules

- 0.5 n = ln (\frac{1}{2})

Solve

- 0.5 n = ln (\frac{1}{2}) : n = \frac{ln ( 2 )}{0.5}

n = \frac{ln ( 2 )}{0.5}

Verify Solutions:

n = \frac{ln ( 2 )}{0.5}

True

The solution is

n = \frac{ln ( 2 )}{0.5}

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What is the answer to (15)/(1+2e^{-0.5n)}=7.5 ?
The answer to (15)/(1+2e^{-0.5n)}=7.5 is n=(ln(2))/(0.5)