What is the answer to 2ln(5-e^{-2x})=1 ?

The answer to 2ln(5-e^{-2x})=1 is x=-(ln(-sqrt(e)+5))/2

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2ln(5-e^{-2x})=1

2 ln (5 - e^{- 2 x}) = 1

x = - \frac{ln ( - e + 5 )}{2}

Decimal Notation

x = - 0.60467 \dots

Solution steps

2 ln (5 - e^{- 2 x}) = 1

Rewrite the equation with

e^{- 2 x} = u

2 ln (5 - u) = 1

Solve

2 ln (5 - u) = 1 : u = - e + 5

u = - e + 5

Substitute back

u = e^{- 2 x},

solve for

x

Solve

e^{- 2 x} = - e + 5 : x = - \frac{ln ( - e + 5 )}{2}

x = - \frac{ln ( - e + 5 )}{2}

27 = 3^{x}

27 = 3^{6 - 3 x}

e^{x} - 2 x e^{x} = 0

x, y = 2^{x}

4 = 3 + x + e^{x}

What is the answer to 2ln(5-e^{-2x})=1 ?
The answer to 2ln(5-e^{-2x})=1 is x=-(ln(-sqrt(e)+5))/2