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

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

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0=2xln(x)+x

0 = 2 x ln (x) + x

x = \frac{1}{e}

Decimal Notation

x = 0.60653 \dots

Solution steps

0 = 2 x ln (x) + x

Switch sides

2 x ln (x) + x = 0

Move

x

to the right side

2 x ln (x) = - x

Move

x

to the left side

2 x ln (x) + x = 0

Factor

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

x (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 = \frac{1}{e}

Verify Solutions:

x = 0

False

, x = \frac{1}{e}

True

The solution is

x = \frac{1}{e}

123 = 10 lo g_{10} (\frac{x}{1})

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

lo g_{a} (64) = 3

ln (- x - 5) = ln (x - 61) - ln (x + 7)

ln (5 x + e) = - 8