What is the answer to roots 5x^4ln(x)+x^4 ?

The answer to roots 5x^4ln(x)+x^4 is x= 1/(\sqrt[5]{e)}

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roots 5x^4ln(x)+x^4

roots

5 x^{4} ln (x) + x^{4}

x = \frac{1}{5 e}

Solution steps

5 x^{4} ln (x) + x^{4}

The roots are the intercepts with the x-axis

(y = 0)

5 x^{4} ln (x) + x^{4} = 0

Move

x^{4}

to the right side

5 x^{4} ln (x) = - x^{4}

Move

x^{4}

to the left side

5 x^{4} ln (x) + x^{4} = 0

Factor

5 x^{4} ln (x) + x^{4} : x^{4} (5 ln (x) + 1)

x^{4} (5 ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 5 ln (x) + 1 = 0

Solve

5 ln (x) + 1 = 0 : x = \frac{1}{5 e}

Verify Solutions:

x = 0

False

, x = \frac{1}{5 e}

True

The solution is

x = \frac{1}{5 e}

ln (x) + ln (x + 10) = 4

3 lo g_{10} (x) = lo g_{10} (125)

\frac{1 + ln ( x )}{2} = 0

lo g_{6} (x^{2} - x - 6) = 2

2 lo g_{2} (x) = 14

What is the answer to roots 5x^4ln(x)+x^4 ?
The answer to roots 5x^4ln(x)+x^4 is x= 1/(\sqrt[5]{e)}