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

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

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

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

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

x = \frac{1}{4 e}

Decimal

x = 0.77880 \dots

Solution steps

x^{3} + 4 x^{3} ln (x) = 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_{10} (2 x - 5) = 0

lo g_{0.2} (3 x - 1) = - 3

lo g_{\frac{1}{4}} (x + 4) = - 1

lo g_{2} (x + 3) = 6

lo g_{3} (n) + lo g_{3} (6) = lo g_{3} (12)

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