What is the answer to x*ln(x)+x=0 ?

The answer to x*ln(x)+x=0 is x= 1/e

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x*ln(x)+x=0

x \cdot ln (x) + x = 0

x = \frac{1}{e}

Decimal Notation

x = 0.36787 \dots

Solution steps

x ln (x) + x = 0

Move

x

to the right side

x ln (x) = - x

Move

x

to the left side

x ln (x) + x = 0

Factor

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

x (ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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}

p, - 100 = 10 lo g_{10} (p)

lo g_{10} (x) = 3.8192

26 ln (4 x - 5) = 3 + ln (e^{10})

x, ln (x) = 1 - v + ln (1 - v)

ln (x) + ln (9 x) = 3