What is the answer to solvefor x,xy+ln(xy)=-1 ?

The answer to solvefor x,xy+ln(xy)=-1 is x=(\W_{0}(1/e))/y

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solvefor x,xy+ln(xy)=-1

solve for

x, x y + ln (x y) = - 1

x = \frac{W _{0} ( \frac{1}{e} )}{y}

Solution steps

x y + ln (x y) = - 1

Move

x y

to the right side

ln (x y) = - 1 - x y

f (x) = g (x),

then

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

e^{l n (x y)} = e^{- 1 - x y}

Simplify

e^{l n (x y)} : x y

x y = e^{- 1 - x y}

Solve

x y = e^{- 1 - x y} : x = \frac{W _{0} ( \frac{1}{e} )}{y}

x = \frac{W _{0} ( \frac{1}{e} )}{y}

Verify Solutions:

x = \frac{W _{0} ( \frac{1}{e} )}{y}

True

The solution is

x = \frac{W _{0} ( \frac{1}{e} )}{y}

ln (\frac{0.43258}{x}) = 0.8915

lo g_{b} (x^{2} - 2) = lo g_{b} (x)

ln (x - 3) = 5

lo g_{\frac{1}{3}} (x) = 243

(lo g_{2} (x))^{2} - 1 = 0

What is the answer to solvefor x,xy+ln(xy)=-1 ?
The answer to solvefor x,xy+ln(xy)=-1 is x=(\W_{0}(1/e))/y