What is the answer to 0=3x^2ln(x)+x^2 ?

The answer to 0=3x^2ln(x)+x^2 is x= 1/(\sqrt[3]{e)}

Solve for x: 0=3x^2ln(x)+x^2

The solution is x= 1/(\sqrt[3]{e)}

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0 = 3 x^{2} ln (x) + x^{2}

x = \frac{1}{3 e}

Decimal

x = 0.71653 \dots

Solution steps

0 = 3 x^{2} ln (x) + x^{2}

Switch sides

3 x^{2} ln (x) + x^{2} = 0

Move

x^{2}

to the right side

3 x^{2} ln (x) = - x^{2}

Move

x^{2}

to the left side

3 x^{2} ln (x) + x^{2} = 0

Factor

3 x^{2} ln (x) + x^{2} : x^{2} (3 ln (x) + 1)

x^{2} (3 ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 3 ln (x) + 1 = 0

Solve

3 ln (x) + 1 = 0 : x = \frac{1}{3 e}

Verify Solutions:

x = 0

False

, x = \frac{1}{3 e}

True

The solution is

x = \frac{1}{3 e}

3 - lo g_{3} (x) - 2 = 0

lo g_{10} (x) (32) = \frac{5}{2}

ln ((x - 4)^{2}) = 12

lo g_{2 x - 2} (3 x^{2} + 2 x - 17) = 2

lo g_{10} (3 x + 1) = 6

What is the answer to 0=3x^2ln(x)+x^2 ?
The answer to 0=3x^2ln(x)+x^2 is x= 1/(\sqrt[3]{e)}
Solve for x: 0=3x^2ln(x)+x^2
The solution is x= 1/(\sqrt[3]{e)}