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

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

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

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

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0 = 2 x + ln (x)

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

Decimal Notation

x = 0.42630 \dots

Solution steps

0 = 2 x + ln (x)

Switch sides

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}

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ln (x^{2} + 2) - ln (x - 4) = 7

0.7 = lo g_{2} (\frac{x}{32000})

lo g_{4} (x + 5) + lo g_{4} (x - 1) = 2