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Popular >

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

Solution

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

Solution

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

+1

Decimal Notation

x = - 1.68437 \dots

Solution steps

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

Rewrite the equation with

e^{- x} = u

ln (2 + u) = 2

Solve

ln (2 + u) = 2 : u = e^{2} - 2

u = e^{2} - 2

Substitute back

u = e^{- x},

solve for

x

Solve

e^{- x} = e^{2} - 2 : x = - ln (e^{2} - 2)

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

Popular Examples

e^{2 x} - 5 e^{x} = - 6

e^{2 x + 1} = 3

e^{- x} = \frac{1}{2}

e^{6x}+10e^{3x}-11=0

e^{6 x} + 10 e^{3 x} - 11 = 0

(\frac{1}{3})^{x} = 27

Frequently Asked Questions (FAQ)

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