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Popular >

xe^x=e^{x-1}

Solution

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

Solution

x = \frac{1}{e}

+1

Decimal

x = 0.36787 \dots

Solution steps

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

Subtract

e^{x - 1}

from both sides

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

Simplify

x e^{x} - e^{x - 1} = 0

Factor

x e^{x} - e^{x - 1} : e^{x} (x - \frac{1}{e})

e^{x} (x - \frac{1}{e}) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

e^{x} = 0 or x - \frac{1}{e} = 0

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

x - \frac{1}{e} = 0 : x = \frac{1}{e}

x = \frac{1}{e}

Graph

Popular Examples

5^{a} = 5

e^{-5x}-5e^{-5x}x=0

e^{- 5 x} - 5 e^{- 5 x} x = 0

(- 1)^{x} = 1

121\times 11^{x-2}=3\times 11^x-22

121 \times 1 1^{x - 2} = 3 \times 1 1^{x} - 22

8^{- 3} = 2^{x + 5}

Frequently Asked Questions (FAQ)

What is the answer to xe^x=e^{x-1} ?
The answer to xe^x=e^{x-1} is x= 1/e