What is the answer to (15)/(1+2e^{-0.5n)}=1.8 ?

The answer to (15)/(1+2e^{-0.5n)}=1.8 is n=-(ln(11/3))/(0.5)

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(15)/(1+2e^{-0.5n)}=1.8

\frac{15}{1 + 2 e ^{- 0.5 n}} = 1.8

n = - \frac{ln ( \frac{11}{3} )}{0.5}

Decimal Notation

n = - 2.59856 \dots

Solution steps

\frac{15}{1 + 2 e ^{- 0.5 n}} = 1.8

Multiply both sides by

1 + 2 e^{- 0.5 n}

\frac{15}{1 + 2 e ^{- 0.5 n}} (1 + 2 e^{- 0.5 n}) = 1.8 (1 + 2 e^{- 0.5 n})

Simplify

15 = 1.8 (1 + 2 e^{- 0.5 n})

Switch sides

1.8 (1 + 2 e^{- 0.5 n}) = 15

Multiply both sides by

10

18 (1 + 2 e^{- 0.5 n}) = 150

Divide both sides by

18

1 + 2 e^{- 0.5 n} = \frac{25}{3}

Move

1

to the right side

2 e^{- 0.5 n} = \frac{22}{3}

Divide both sides by

2

e^{- 0.5 n} = \frac{11}{3}

Apply exponent rules

- 0.5 n = ln (\frac{11}{3})

Solve

- 0.5 n = ln (\frac{11}{3}) : n = - \frac{ln ( \frac{11}{3} )}{0.5}

n = - \frac{ln ( \frac{11}{3} )}{0.5}

Verify Solutions:

n = - \frac{ln ( \frac{11}{3} )}{0.5}

True

The solution is

n = - \frac{ln ( \frac{11}{3} )}{0.5}

(2 x - 5)^{x} = (2 x - 5)^{3 x - 4}

x e^{x} + 2 e^{x} = 0

(2^{x})^{3} = 8^{- x + 3}

e^{x} = 28

2 e^{x} - 9 e^{x} + 4 = 0

What is the answer to (15)/(1+2e^{-0.5n)}=1.8 ?
The answer to (15)/(1+2e^{-0.5n)}=1.8 is n=-(ln(11/3))/(0.5)