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

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

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0=2xln(x/2)+x

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

x = \frac{2}{e}

Decimal Notation

x = 1.21306 \dots

Solution steps

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

Switch sides

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

Move

x

to the right side

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

Move

x

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

Verify Solutions:

x = 0

False

, x = \frac{2}{e}

True

The solution is

x = \frac{2}{e}

4 - 2 \cdot lo g_{3} (x) = 3

2 lo g_{7} (2 x - 1) - 5 = 9

ln (c) + ln (c) = 1

x, 20 lo g_{10} (x) = 40

lo g_{6} (x) = 32

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