What is the answer to (e^x)/(1+e^x)=0.1 ?

The answer to (e^x)/(1+e^x)=0.1 is x=-2ln(3)

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(e^x)/(1+e^x)=0.1

\frac{e ^{x}}{1 + e ^{x}} = 0.1

x = - 2 ln (3)

Decimal Notation

x = - 2.19722 \dots

Solution steps

\frac{e ^{x}}{1 + e ^{x}} = 0.1

Multiply both sides by

1 + e^{x}

\frac{e ^{x}}{1 + e ^{x}} (1 + e^{x}) = 0.1 (1 + e^{x})

Simplify

e^{x} = 0.1 (1 + e^{x})

Multiply both sides by

10

e^{x} \cdot 10 = 1 + e^{x}

Move

e^{x}

to the left side

9 e^{x} = 1

Divide both sides by

9

e^{x} = \frac{1}{9}

Apply exponent rules

x = - 2 ln (3)

Verify Solutions:

x = - 2 ln (3)

True

The solution is

x = - 2 ln (3)

- 12 e^{- x} = 0

5^{x - 2} + 5^{x} + 5^{x + 1} = 30

2 5^{x} - 1 5^{x} = 9^{x}

y, x = e^{3 y}

5^{x} + 8 = 26

What is the answer to (e^x)/(1+e^x)=0.1 ?
The answer to (e^x)/(1+e^x)=0.1 is x=-2ln(3)