What is the answer to solvefor y,x=4e^y+y-7 ?

The answer to solvefor y,x=4e^y+y-7 is y=-\W(4/(e^{-x-7)})+x+7

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solvefor y,x=4e^y+y-7

solve for

y, x = 4 e^{y} + y - 7

y = - W (\frac{4}{e ^{- x - 7}}) + x + 7

Solution steps

x = 4 e^{y} + y - 7

Prepare

x = 4 e^{y} + y - 7

for Lambert form:

4 = (x - y + 7) e^{- y}

Rewrite the equation with

- y + x + 7 = u

and

y = - u + x + 7

4 = (x - (- u + x + 7) + 7) e^{- (- u + x + 7)}

Simplify

4 = e^{u - x - 7} u

Rewrite

4 = e^{u - x - 7} u

in Lambert form:

e^{u} u = \frac{4}{e ^{- x - 7}}

Solve

e^{u} u = \frac{4}{e ^{- x - 7}} : u = W (\frac{4}{e ^{- x - 7}})

u = W (\frac{4}{e ^{- x - 7}})

Substitute back

u = - y + x + 7,

solve for

y

Solve

- y + x + 7 = W (\frac{4}{e ^{- x - 7}}) : y = - W (\frac{4}{e ^{- x - 7}}) + x + 7

y = - W (\frac{4}{e ^{- x - 7}}) + x + 7

3^{3 x - 4} = 21

3^{3 x - 4} = 24

3 = 20 (\frac{1}{2})^{2 x}

4^{x + 1} + 2^{2 x} = 20

7^{x + 1} - 2 = 0

What is the answer to solvefor y,x=4e^y+y-7 ?
The answer to solvefor y,x=4e^y+y-7 is y=-\W(4/(e^{-x-7)})+x+7