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

The answer to x/2 =xln(x^2) is x=\sqrt[4]{e},x=-\sqrt[4]{e}

Solve for x: x/2 =xln(x^2)

The solution is x=\sqrt[4]{e},x=-\sqrt[4]{e}

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\frac{x}{2} = x ln (x^{2})

x = 4 e, x = - 4 e

Decimal

x = 1.28402 \dots, x = - 1.28402 \dots

Solution steps

\frac{x}{2} = x ln (x^{2})

Switch sides

x ln (x^{2}) = \frac{x}{2}

Multiply both sides by

2

x ln (x^{2}) \cdot 2 = \frac{x}{2} \cdot 2

Simplify

x ln (x^{2}) \cdot 2 = x

Move

x

to the left side

x ln (x^{2}) \cdot 2 - x = 0

Factor

x ln (x^{2}) \cdot 2 - x : x (2 ln (x^{2}) - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

2 ln (x^{2}) - 1 = 0 : x = 4 e, x = - 4 e

Verify Solutions:

x = 0

False

, x = 4 e

True

, x = - 4 e

True

The solutions are

x = 4 e, x = - 4 e

\frac{ln ( x ^{3} )}{4} = (ln (x))^{3}

3 - lo g_{2} (5 x - 2) = 0

lo g_{11} (x) = 2

ln (x (x - 2)) = 0

lo g_{5} (x^{2} - 2 x - 10) = 2

What is the answer to x/2 =xln(x^2) ?
The answer to x/2 =xln(x^2) is x=\sqrt[4]{e},x=-\sqrt[4]{e}
Solve for x: x/2 =xln(x^2)
The solution is x=\sqrt[4]{e},x=-\sqrt[4]{e}