What is the answer to 4x^3ln(x)+x^3=0 ?

The answer to 4x^3ln(x)+x^3=0 is x= 1/(\sqrt[4]{e)}

Solve for x: 4x^3ln(x)+x^3=0

The solution is x= 1/(\sqrt[4]{e)}

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4 x^{3} ln (x) + x^{3} = 0

x = \frac{1}{4 e}

Decimal

x = 0.77880 \dots

Solution steps

4 x^{3} ln (x) + x^{3} = 0

Move

x^{3}

to the right side

4 x^{3} ln (x) = - x^{3}

Move

x^{3}

to the left side

4 x^{3} ln (x) + x^{3} = 0

Factor

4 x^{3} ln (x) + x^{3} : x^{3} (4 ln (x) + 1)

x^{3} (4 ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 4 ln (x) + 1 = 0

Solve

4 ln (x) + 1 = 0 : x = \frac{1}{4 e}

Verify Solutions:

x = 0

False

, x = \frac{1}{4 e}

True

The solution is

x = \frac{1}{4 e}

- lo g_{3} (2 - x) = 3

ln (x^{2} - 16) = 0

- 6 lo g_{12} (x - 5) = - 6

2 \cdot lo g_{2} (3 x - 7) = 10

2 lo g_{10} (x) - lo g_{10} (6) = lo g_{10} (486)

What is the answer to 4x^3ln(x)+x^3=0 ?
The answer to 4x^3ln(x)+x^3=0 is x= 1/(\sqrt[4]{e)}
Solve for x: 4x^3ln(x)+x^3=0
The solution is x= 1/(\sqrt[4]{e)}