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Popular >

e^x=xe^x

Solution

e^{x} = x e^{x}

Solution

x = 1

Solution steps

e^{x} = x e^{x}

Subtract

x e^{x}

from both sides

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

Simplify

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

Factor

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

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

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

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

1 - x = 0 : x = 1

x = 1

Popular Examples

e^{x} = 11

e^{x} = 34

5^{- x} = \frac{1}{125}

2^{x} = 5^{x - 1}

solvefor t,a=b^t solve for

t, a = b^{t}

Frequently Asked Questions (FAQ)

What is the answer to e^x=xe^x ?
The answer to e^x=xe^x is x=1