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

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

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(2x)(ln(x))-x=0

(2 x) (ln (x)) - x = 0

x = e

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 = e

Verify Solutions:

x = 0

False

, x = e

True

The solution is

x = e

x, lo g_{x} (3 x - y) = 2

lo g_{3} (5 x) = 4

lo g_{2} (x) + lo g_{4} (x^{2}) = 4

1 + lo g_{10} (3 x - 4) = 0

ln (x^{5}) - ln (x^{3}) - 4 = 0

What is the answer to (2x)(ln(x))-x=0 ?
The answer to (2x)(ln(x))-x=0 is x=sqrt(e)
Solve for x: (2x)(ln(x))-x=0
The solution is x=sqrt(e)