What is the answer to solvefor x,ln(x)+ln(y)+xy=3 ?

The answer to solvefor x,ln(x)+ln(y)+xy=3 is x=(\W_{0}(e^3))/y

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solvefor x,ln(x)+ln(y)+xy=3

solve for

x, ln (x) + ln (y) + x y = 3

x = \frac{W _{0} ( e ^{3} )}{y}

Solution steps

ln (x) + ln (y) + x y = 3

Move

ln (y)

to the right side

ln (x) + x y = 3 - ln (y)

Move

x y

to the right side

ln (x) = 3 - ln (y) - x y

f (x) = g (x),

then

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

e^{l n (x)} = e^{3 - l n (y) - x y}

Simplify

e^{l n (x)} : x

Simplify

e^{3 - l n (y) - x y} : \frac{e ^{3 - x y}}{y}

x = \frac{e ^{3 - x y}}{y}

Multiply both sides by

y

x y = \frac{e ^{3 - x y}}{y} y

Simplify

x y = e^{3 - x y}

Solve

x y = e^{3 - x y} : x = \frac{W _{0} ( e ^{3} )}{y}

x = \frac{W _{0} ( e ^{3} )}{y}

Verify Solutions:

x = \frac{W _{0} ( e ^{3} )}{y}

True

The solution is

x = \frac{W _{0} ( e ^{3} )}{y}

x, ln (x^{2}) = 18

ln (t) = 0.96 ln (16) + 0.2

x, ln (x^{2}) = 20

lo g_{9} (x) = \frac{- 3}{2}

lo g_{5 - x} (x^{2} - 2 x + 65) = 2

What is the answer to solvefor x,ln(x)+ln(y)+xy=3 ?
The answer to solvefor x,ln(x)+ln(y)+xy=3 is x=(\W_{0}(e^3))/y