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

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

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2xln(x)+x=0

2 x ln (x) + x = 0

x = \frac{1}{e}

Decimal Notation

x = 0.60653 \dots

Solution steps

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}

lo g_{10} (x) + lo g_{10} (20) = 3

lo g_{x} (1000) = 3

lo g_{2} (2^{x + 1} - 322) = x

ln (y - 1) = 1 + ln (3 y + 2)

lo g_{3} (x + 1) = 3