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Popular >

xe^{2x}-xe^x-6x=0

Solution

x e^{2 x} - x e^{x} - 6 x = 0

Solution

x = 0, x = ln (3)

+1

Decimal Notation

x = 0, x = 1.09861 \dots

Solution steps

x e^{2 x} - x e^{x} - 6 x = 0

Factor

x e^{2 x} - x e^{x} - 6 x : x (e^{x} + 2) (e^{x} - 3)

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

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

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

Solve

e^{x} + 2 = 0 :

No Solution for

x \in R

Solve

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

x = 0, x = ln (3)

Popular Examples

e^{2 x} = e^{x} + 6

(100)/(1+15e^{-0.4x)}=20

\frac{100}{1 + 15 e ^{- 0.4 x}} = 20

3^{x-4}=8^{2x+2}

3^{x - 4} = 8^{2 x + 2}

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

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

49^x=343^{2x-3}

4 9^{x} = 34 3^{2 x - 3}

Frequently Asked Questions (FAQ)

What is the answer to xe^{2x}-xe^x-6x=0 ?
The answer to xe^{2x}-xe^x-6x=0 is x=0,x=ln(3)