What is the answer to x^2ln(x)-(x^2)/2 =0 ?

The answer to x^2ln(x)-(x^2)/2 =0 is x=sqrt(e)

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x^2ln(x)-(x^2)/2 =0

Solution

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

Solution

x = e

Decimal Notation

x = 1.64872 \dots

Solution steps

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

Move

\frac{x ^{2}}{2}

to the right side

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

Multiply both sides by

2

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

Simplify

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

Move

x^{2}

to the left side

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

Factor

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

Popular Examples

solvefor x,log_{x}(y)=5 solve for

x, lo g_{x} (y) = 5

solvefor x,-1000000=ln(x)-x solve for

x, - 1000000 = ln (x) - x

solvefor x,log_{x}(y)=0 solve for

x, lo g_{x} (y) = 0

log_{3}(x^2)+log_{3}(9)=4

lo g_{3} (x^{2}) + lo g_{3} (9) = 4

log_{2x}(16)=2

lo g_{2 x} (16) = 2

Frequently Asked Questions (FAQ)

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

x^2ln(x)-(x^2)/2 =0

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to x^2ln(x)-(x^2)/2 =0 ?

Solve for x: x^2ln(x)-(x^2)/2 =0