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Popular >

5=5e^{-x}-5xe^{-x}

Solution

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

Solution

x = 0

Solution steps

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

Prepare

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

for Lambert form:

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

Rewrite the equation with

- x + 1 = u

and

x = - u + 1

5 = 5 e^{- (- u + 1)} (1 - (- u + 1))

Simplify

5 = 5 e^{u - 1} u

Rewrite

5 = 5 e^{u - 1} u

in Lambert form:

e^{u} u = e

Solve

e^{u} u = e : u = 1

u = 1

Substitute back

u = - x + 1,

solve for

x

Solve

- x + 1 = 1 : x = 0

x = 0

Popular Examples

10^{7x+35}=10^{2x+5}

1 0^{7 x + 35} = 1 0^{2 x + 5}

3 6^{3 x + 1} = 121

2^{3 x - 4} = 3

2^{3 x - 4} = 5

3^x-3^{x-1}+3^{x-2}=21

3^{x} - 3^{x - 1} + 3^{x - 2} = 21

Frequently Asked Questions (FAQ)

What is the answer to 5=5e^{-x}-5xe^{-x} ?
The answer to 5=5e^{-x}-5xe^{-x} is x=0