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

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

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

The solution is x= 1/(2sqrt(e))

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0 = 2 x ln (2 x) + x

x = \frac{1}{2 e}

Decimal Notation

x = 0.30326 \dots

Solution steps

0 = 2 x ln (2 x) + x

Switch sides

2 x ln (2 x) + x = 0

Move

x

to the right side

2 x ln (2 x) = - x

Move

x

to the left side

2 x ln (2 x) + x = 0

Factor

2 x ln (2 x) + x : x (2 ln (2 x) + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Verify Solutions:

x = 0

False

, x = \frac{1}{2 e}

True

The solution is

x = \frac{1}{2 e}

lo g_{10} (\frac{4 x}{2}) = 2

4 ln (7 x - 8) - 13 = - 25

ln (x + 63) - ln (5 - 4 x) = 6 ln (2)

lo g_{81} (x) = \frac{3}{4}

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

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