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

The answer to xln(x)-x=0 is x=e

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xln(x)-x=0

x ln (x) - x = 0

x = e

Decimal Notation

x = 2.71828 \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 = e

Verify Solutions:

x = 0

False

, x = e

True

The solution is

x = e

- 1 - ln (2 + x) = 0

ln (\frac{1}{x}) = - ln (x)

8 ln (x) = 1

lo g_{10} (x) = 1.709

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