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Popular >

xe^{2x}=xe^{x+3}

Solution

x e^{2 x} = x e^{x + 3}

Solution

x = 0, x = 3

Solution steps

x e^{2 x} = x e^{x + 3}

Subtract

x e^{x + 3}

from both sides

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

Simplify

x e^{2 x} - x e^{x + 3} = 0

Factor

x e^{2 x} - x e^{x + 3} : e^{x} x (e^{x} - e^{3})

e^{x} x (e^{x} - e^{3}) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

e^{x} = 0 or x = 0 or e^{x} - e^{3} = 0

Solve

e^{x} = 0 :

No Solution for

x \in R

Solve

e^{x} - e^{3} = 0 : x = 3

x = 0, x = 3

Popular Examples

3^{3n}*9^{-2n+1}=27

3^{3 n} \cdot 9^{- 2 n + 1} = 27

2 = 1. 1^{t}

15=45e^{-0.05t}

15 = 45 e^{- 0.05 t}

3^{4x-2}=9^{-(x+1)}

3^{4 x - 2} = 9^{- (x + 1)}

2xe^{x^2}=x^2e^{x^2}

2 x e^{x^{2}} = x^{2} e^{x^{2}}

Frequently Asked Questions (FAQ)

What is the answer to xe^{2x}=xe^{x+3} ?
The answer to xe^{2x}=xe^{x+3} is x=0,x=3