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Popular >

(e^x)/(1+e^x)=0.5

Solution

\frac{e ^{x}}{1 + e ^{x}} = 0.5

Solution

x = 0

Solution steps

\frac{e ^{x}}{1 + e ^{x}} = 0.5

Multiply both sides by

1 + e^{x}

\frac{e ^{x}}{1 + e ^{x}} (1 + e^{x}) = 0.5 (1 + e^{x})

Simplify

e^{x} = 0.5 (1 + e^{x})

Multiply both sides by

10

e^{x} \cdot 10 = 5 (1 + e^{x})

Expand

5 (1 + e^{x}) : 5 + 5 e^{x}

e^{x} \cdot 10 = 5 + 5 e^{x}

Move

5 e^{x}

to the left side

5 e^{x} = 5

Divide both sides by

5

e^{x} = 1

Apply exponent rules

x = 0

Verify Solutions:

x = 0

True

The solution is

x = 0

Popular Examples

5^{x - 2} = 3^{- x}

5^{x} - 5^{- x} = 8

6^{x-1}=8^{2-x}

6^{x - 1} = 8^{2 - x}

6^{3x+2}=36^{x-6}

6^{3 x + 2} = 3 6^{x - 6}

2 (5^{x}) = 32

Frequently Asked Questions (FAQ)

What is the answer to (e^x)/(1+e^x)=0.5 ?
The answer to (e^x)/(1+e^x)=0.5 is x=0