What is the answer to 4e^{-x}x^3-e^{-x}x^4=0 ?

The answer to 4e^{-x}x^3-e^{-x}x^4=0 is x=0,x=4

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4e^{-x}x^3-e^{-x}x^4=0

4 e^{- x} x^{3} - e^{- x} x^{4} = 0

x = 0, x = 4

Solution steps

4 e^{- x} x^{3} - e^{- x} x^{4} = 0

Factor

4 e^{- x} x^{3} - e^{- x} x^{4} : e^{- x} x^{3} (4 - x)

e^{- x} x^{3} (4 - x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{- x} = 0 or x = 0 or 4 - x = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

4 - x = 0 : x = 4

x = 0, x = 4

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

5^{x + 3} - 5^{x - 1} - 3120 = 0

1 0^{2 x - 3} = \frac{1}{10}

9^{3 x - 7} = 9^{5 - x}

ln (9 e^{2 x}) = 1

What is the answer to 4e^{-x}x^3-e^{-x}x^4=0 ?
The answer to 4e^{-x}x^3-e^{-x}x^4=0 is x=0,x=4