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Popular >

3-x=3e^{-x}

Solution

3 - x = 3 e^{- x}

Solution

x = 0, x = W_{0} (- \frac{3}{e ^{3}}) + 3

+1

Decimal Notation

x = 0, x = 2.82143 \dots

Solution steps

3 - x = 3 e^{- x}

Prepare

3 - x = 3 e^{- x}

for Lambert form:

(3 - x) e^{x} = 3

Rewrite the equation with

x - 3 = u

and

x = u + 3

(3 - (u + 3)) e^{(u + 3)} = 3

Simplify

- e^{u + 3} u = 3

Rewrite

- e^{u + 3} u = 3

in Lambert form:

e^{u} u = - \frac{3}{e ^{3}}

Solve

e^{u} u = - \frac{3}{e ^{3}} : u = - 3, u = W_{0} (- \frac{3}{e ^{3}})

u = - 3, u = W_{0} (- \frac{3}{e ^{3}})

Substitute back

u = x - 3,

solve for

x

Solve

x - 3 = - 3 : x = 0

Solve

x - 3 = W_{0} (- \frac{3}{e ^{3}}) : x = W_{0} (- \frac{3}{e ^{3}}) + 3

x = 0, x = W_{0} (- \frac{3}{e ^{3}}) + 3

Popular Examples

∣ 2 (3^{x}) - 4 ∣ = 8

solvefor t,e^{-4u}=e^{2t}solve for

t, e^{- 4 u} = e^{2 t}

3^{x} + 3^{2 x + 1} = 4

2^{2x-1}=3^{x+1}

2^{2 x - 1} = 3^{x + 1}

5^{x+1}+5+5^{x-1}= 31/5

5^{x + 1} + 5 + 5^{x - 1} = \frac{31}{5}

Frequently Asked Questions (FAQ)

What is the answer to 3-x=3e^{-x} ?
The answer to 3-x=3e^{-x} is x=0,x=\W_{0}(-3/(e^3))+3