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

The answer to x^2=2x^2ln(x) is x=sqrt(e)

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x^2=2x^2ln(x)

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

x = e

Decimal Notation

x = 1.64872 \dots

Solution steps

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

Switch sides

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

Move

x^{2}

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 ln (x) - 1 = 0

Solve

2 ln (x) - 1 = 0 : x = e

Verify Solutions:

x = 0

False

, x = e

True

The solution is

x = e

- ln (2 + x) = 2

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

y, ln (y) = 0

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

ln (x) = 11.93