What is the answer to 2xln(1/x)-x=0 ?

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

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2xln(1/x)-x=0

Solution

2 x ln (\frac{1}{x}) - x = 0

Solution

x = \frac{1}{e}

Decimal

x = 0.60653 \dots

Solution steps

2 x ln (\frac{1}{x}) - x = 0

Move

x

to the right side

2 x ln (\frac{1}{x}) = x

Move

x

to the left side

2 x ln (\frac{1}{x}) - x = 0

Factor

2 x ln (\frac{1}{x}) - x : x (2 ln (\frac{1}{x}) - 1)

x (2 ln (\frac{1}{x}) - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Verify Solutions:

x = 0

False

, x = \frac{1}{e}

True

The solution is

x = \frac{1}{e}

Graph

Popular Examples

log_{10}(2x-6)=2

lo g_{10} (2 x - 6) = 2

log_{256}(x)=-3/4

lo g_{256} (x) = - \frac{3}{4}

x(2ln(x)+1)=0

x (2 ln (x) + 1) = 0

log_{2}(x)-3log_{10}(x)=2

lo g_{2} (x) - 3 lo g_{10} (x) = 2

log_{sqrt(5)}(x)=0

lo g_{5} (x) = 0

Frequently Asked Questions (FAQ)

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

2xln(1/x)-x=0

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

What is the answer to 2xln(1/x)-x=0 ?

Solve for x: 2xln(1/x)-x=0