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Popular >

e^{-x}+2=x

Solution

e^{- x} + 2 = x

Solution

x = W_{0} (\frac{1}{e ^{2}}) + 2

+1

Decimal Notation

x = 2.12002 \dots

Solution steps

e^{- x} + 2 = x

Prepare

e^{- x} + 2 = x

for Lambert form:

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

Rewrite the equation with

x - 2 = u

and

x = u + 2

1 = ((u + 2) - 2) e^{(u + 2)}

Simplify

1 = e^{u + 2} u

Rewrite

1 = e^{u + 2} u

in Lambert form:

e^{u} u = \frac{1}{e ^{2}}

Solve

e^{u} u = \frac{1}{e ^{2}} : u = W_{0} (\frac{1}{e ^{2}})

u = W_{0} (\frac{1}{e ^{2}})

Substitute back

u = x - 2,

solve for

x

Solve

x - 2 = W_{0} (\frac{1}{e ^{2}}) : x = W_{0} (\frac{1}{e ^{2}}) + 2

x = W_{0} (\frac{1}{e ^{2}}) + 2

Popular Examples

N=N_{0}e^{λ*t}

N = N_{0} e^{λ \cdot t}

2^{- x} = x - 9

2^{x - 3} = \frac{1}{8}

90-0.04x=30e^{0.001x}

90 - 0.04 x = 30 e^{0.001 x}

5^{n} = 1

Frequently Asked Questions (FAQ)

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