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

The answer to x-2xln(x)=0 is x=sqrt(e)

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x-2xln(x)=0

x - 2 x ln (x) = 0

x = e

Decimal Notation

x = 1.64872 \dots

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 = e

Verify Solutions:

x = 0

False

, x = e

True

The solution is

x = e

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ln (x) - ln (x - 2000) = 14876

lo g_{2} (2 x + 1) - lo g_{2} (x + 2) = 3

2 lo g_{3} (x) = lo g_{3} (16)