What is the answer to (e^x)/(1+e^x)=0.9 ?

The answer to (e^x)/(1+e^x)=0.9 is x=2ln(3)

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(e^x)/(1+e^x)=0.9

\frac{e ^{x}}{1 + e ^{x}} = 0.9

x = 2 ln (3)

Decimal Notation

x = 2.19722 \dots

Solution steps

\frac{e ^{x}}{1 + e ^{x}} = 0.9

Multiply both sides by

1 + e^{x}

\frac{e ^{x}}{1 + e ^{x}} (1 + e^{x}) = 0.9 (1 + e^{x})

Simplify

e^{x} = 0.9 (1 + e^{x})

Multiply both sides by

10

e^{x} \cdot 10 = 9 (1 + e^{x})

Expand

9 (1 + e^{x}) : 9 + 9 e^{x}

e^{x} \cdot 10 = 9 + 9 e^{x}

Move

9 e^{x}

to the left side

e^{x} = 9

Apply exponent rules

x = 2 ln (3)

Verify Solutions:

x = 2 ln (3)

True

The solution is

x = 2 ln (3)

y, \frac{3 ^{y + 1}}{32} = 9 6^{x}

3^{3 x + 2} = 3

y, x = \frac{1 + e ^{y}}{1 - e ^{y}}

5 (2)^{8 t} = 15

9 e^{x} = 1

What is the answer to (e^x)/(1+e^x)=0.9 ?
The answer to (e^x)/(1+e^x)=0.9 is x=2ln(3)