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Popular >

ln(1+e^{-x})+2x=0

Solution

ln (1 + e^{- x}) + 2 x = 0

Solution

x = ln (\frac{- 1 + 5}{2})

+1

Decimal Notation

x = - 0.48121 \dots

Solution steps

ln (1 + e^{- x}) + 2 x = 0

Move

2 x

to the right side

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

If

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (1 + e^{- x})} = e^{- 2 x}

Simplify

e^{l n (1 + e^{- x})} : 1 + e^{- x}

1 + e^{- x} = e^{- 2 x}

Solve

1 + e^{- x} = e^{- 2 x} : x = ln (\frac{- 1 + 5}{2})

x = ln (\frac{- 1 + 5}{2})

Verify Solutions:

x = ln (\frac{- 1 + 5}{2})

True

The solution is

x = ln (\frac{- 1 + 5}{2})

Popular Examples

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y, ln (y) = - ln (x) + c

log_{2}(x+1)-log_{4}(x-3)=2

lo g_{2} (x + 1) - lo g_{4} (x - 3) = 2

lo g_{x} (3) = - 2

log_{2}(sqrt(4x-3))=1

lo g_{2} (4 x - 3) = 1

Frequently Asked Questions (FAQ)

What is the answer to ln(1+e^{-x})+2x=0 ?
The answer to ln(1+e^{-x})+2x=0 is x=ln((-1+sqrt(5))/2)