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

The answer to 2x+ln(x)=0 is x=(\W_{0}(2))/2

Solve for x: 2x+ln(x)=0

The solution is x=(\W_{0}(2))/2

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2 x + ln (x) = 0

x = \frac{W _{0} ( 2 )}{2}

Decimal Notation

x = 0.42630 \dots

Solution steps

2 x + ln (x) = 0

Move

2 x

to the right side

ln (x) = - 2 x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x)} = e^{- 2 x}

Simplify

e^{l n (x)} : x

x = e^{- 2 x}

Solve

x = e^{- 2 x} : x = \frac{W _{0} ( 2 )}{2}

x = \frac{W _{0} ( 2 )}{2}

Verify Solutions:

x = \frac{W _{0} ( 2 )}{2}

True

The solution is

x = \frac{W _{0} ( 2 )}{2}

w, 0 = 20 lo g_{10} (w)

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

lo g_{6} (x + 9) - lo g_{36} (x) = 1

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

3 ln (5 x) = 15