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

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

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x+2xln(x)=0

x + 2 x ln (x) = 0

x = \frac{1}{e}

Solution steps

x + 2 x ln (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}

3 ln (p) - 2 lo g_{p} (e) = 4

ln (x) = 7.1205

lo g_{2} (x + 2) = e

7 lo g_{4} (3 w + 1) + 4 = 25

x^{2} = e^{2 l n (x)}