What is the answer to solvefor y,e^{x+y}=xy ?

The answer to solvefor y,e^{x+y}=xy is y=-\W(-(e^x)/x)

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solvefor y,e^{x+y}=xy

solve for

y, e^{x + y} = x y

y = - W (- \frac{e ^{x}}{x})

Solution steps

e^{x + y} = x y

Prepare

e^{x + y} = x y

for Lambert form:

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

Rewrite the equation with

- y = u

and

y = - u

1 = x (- u) e^{- x - (- u)}

Simplify

1 = - e^{- x + u} xu

Rewrite

1 = - e^{- x + u} xu

in Lambert form:

e^{u} u = - \frac{e ^{x}}{x}

Solve

e^{u} u = - \frac{e ^{x}}{x} : u = W (- \frac{e ^{x}}{x})

u = W (- \frac{e ^{x}}{x})

Substitute back

u = - y,

solve for

y

Solve

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

y = - W (- \frac{e ^{x}}{x})

x, 9 \cdot 2^{x} = 6^{x}

x, 8^{8 x - 6} = 3^{9 x - 10}

9 \cdot 2^{2 x} = 64

x, P a^{x} = Q b^{x}

1 2^{x} = 14 4^{x - 3}

What is the answer to solvefor y,e^{x+y}=xy ?
The answer to solvefor y,e^{x+y}=xy is y=-\W(-(e^x)/x)