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Popular >

x^6e^{-4ln(x)}=2x+15

Solution

x^{6} e^{- 4 l n (x)} = 2 x + 15

Solution

x = 5

Solution steps

x^{6} e^{- 4 l n (x)} = 2 x + 15

Divide both sides by

x^{6}

e^{- 4 l n (x)} = \frac{2 x + 15}{x ^{6}}

Apply log rules

e^{0} = \frac{2 x + 15}{x ^{6}} x^{4}

Multiply both sides by

x^{6}

e^{0} x^{6} = \frac{2 x + 15}{x ^{6}} x^{4} x^{6}

Simplify

\frac{2 x + 15}{x ^{6}} x^{4} x^{6} : x^{4} (2 x + 15)

x^{6} = x^{4} (2 x + 15)

Solve

x^{6} = x^{4} (2 x + 15) : x = 0, x = - 3, x = 5

x = 0, x = - 3, x = 5

Verify Solutions:

x = 0

False

, x = - 3

False

, x = 5

True

The solution is

x = 5

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Frequently Asked Questions (FAQ)

What is the answer to x^6e^{-4ln(x)}=2x+15 ?
The answer to x^6e^{-4ln(x)}=2x+15 is x=5