What is the answer to 1/(e^{-x)+2}=0.3 ?

The answer to 1/(e^{-x)+2}=0.3 is x=-ln(4/3)

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1/(e^{-x)+2}=0.3

\frac{1}{e ^{- x} + 2} = 0.3

x = - ln (\frac{4}{3})

Decimal Notation

x = - 0.28768 \dots

Solution steps

\frac{1}{e ^{- x} + 2} = 0.3

Multiply both sides by

e^{- x} + 2

\frac{1}{e ^{- x} + 2} (e^{- x} + 2) = 0.3 (e^{- x} + 2)

Simplify

1 = 0.3 (e^{- x} + 2)

Switch sides

0.3 (e^{- x} + 2) = 1

Multiply both sides by

10

3 (e^{- x} + 2) = 10

Divide both sides by

3

e^{- x} + 2 = \frac{10}{3}

Move

2

to the right side

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

Apply exponent rules

- x = ln (\frac{4}{3})

Solve

- x = ln (\frac{4}{3}) : x = - ln (\frac{4}{3})

x = - ln (\frac{4}{3})

Verify Solutions:

x = - ln (\frac{4}{3})

True

The solution is

x = - ln (\frac{4}{3})

2 = 1.003 8^{12 \cdot t}

e^{x^{2} + 2 x + 1} = e

6 4^{x} = 4^{4 x + 1}

3^{x + 2} = 4 x

3 \cdot 4^{x} = 2^{2 x + 1}

What is the answer to 1/(e^{-x)+2}=0.3 ?
The answer to 1/(e^{-x)+2}=0.3 is x=-ln(4/3)