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Popular >

xe^x=e^x

Solution

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

Solution

x = 1

Solution steps

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

Subtract

e^{x}

from both sides

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

Simplify

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

Factor

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

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

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

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

x - 1 = 0 : x = 1

x = 1

Popular Examples

2^{2x+1}-3*2^x-2=0

2^{2 x + 1} - 3 \cdot 2^{x} - 2 = 0

sqrt(2^x)= 1/512

2^{x} = \frac{1}{512}

1 0^{x} = 23

solvefor x,e^x-5=0 solve for

x, e^{x} - 5 = 0

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

Frequently Asked Questions (FAQ)

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