What is the answer to (e^{2x})/(3+e^{2x)}= 1/2 ?

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

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(e^{2x})/(3+e^{2x)}= 1/2

\frac{e ^{2 x}}{3 + e ^{2 x}} = \frac{1}{2}

x = \frac{ln ( 3 )}{2}

Decimal

x = 0.54930 \dots

Solution steps

\frac{e ^{2 x}}{3 + e ^{2 x}} = \frac{1}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

e^{2 x} \cdot 2 = (3 + e^{2 x}) \cdot 1

Simplify

e^{2 x} \cdot 2 = 3 + e^{2 x}

Move

e^{2 x}

to the left side

e^{2 x} = 3

Apply exponent rules

2 x = ln (3)

Solve

2 x = ln (3) : x = \frac{ln ( 3 )}{2}

x = \frac{ln ( 3 )}{2}

Verify Solutions:

x = \frac{ln ( 3 )}{2}

True

The solution is

x = \frac{ln ( 3 )}{2}

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

\frac{1}{4} = 6 4^{x}

e^{- x} - x

\frac{100}{e ^{2 x}} = \frac{300}{e ^{4 x}}

5^{2 x} - 2 \times 5^{x} - 15 = 0

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