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

The answer to 2xln(x^2)+2x=0 is x=sqrt(1/e),x=-sqrt(1/e)

Solve for x: 2xln(x^2)+2x=0

The solution is x=sqrt(1/e),x=-sqrt(1/e)

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

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

Decimal

x = 0.60653 \dots, x = - 0.60653 \dots

Solution steps

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

Move

2 x

to the right side

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

Move

2 x

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

ln (x^{2}) + 1 = 0 : x = \frac{1}{e}, x = - \frac{1}{e}

Verify Solutions:

x = 0

False

, x = \frac{1}{e}

True

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

True

The solutions are

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

lo g_{2} (x - 1) = \frac{1}{6}

lo g_{10} (x) + lo g_{10} (x + 15) = 2

lo g_{e} (2 x - 1) = - 3

lo g_{4} (x) = x + 2

lo g_{5} (5 - x) = 2 lo g_{5} (3)

What is the answer to 2xln(x^2)+2x=0 ?
The answer to 2xln(x^2)+2x=0 is x=sqrt(1/e),x=-sqrt(1/e)
Solve for x: 2xln(x^2)+2x=0
The solution is x=sqrt(1/e),x=-sqrt(1/e)