What is the answer to solvefor y,7x+6y=e^y ?

The answer to solvefor y,7x+6y=e^y is y=-(6\W(-1/(6e^{\frac{7x){6}}})+7x)/6

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solvefor y,7x+6y=e^y

solve for

y, 7 x + 6 y = e^{y}

y = - \frac{6 W ( - \frac{1}{6 e ^{\frac{7 x}{6}}} ) + 7 x}{6}

Solution steps

7 x + 6 y = e^{y}

Prepare

7 x + 6 y = e^{y}

for Lambert form:

(7 x + 6 y) e^{- y} = 1

Rewrite the equation with

- y - \frac{7}{6} x = u

and

y = - \frac{6 u + 7 x}{6}

(7 x + 6 (- \frac{6 u + 7 x}{6})) e^{- (- \frac{6 u + 7 x}{6})} = 1

Simplify

- 6 e^{\frac{6 u + 7 x}{6}} u = 1

Rewrite

- 6 e^{\frac{6 u + 7 x}{6}} u = 1

in Lambert form:

e^{u} u = - \frac{1}{6 e ^{\frac{7 x}{6}}}

Solve

e^{u} u = - \frac{1}{6 e ^{\frac{7 x}{6}}} : u = W (- \frac{1}{6 e ^{\frac{7 x}{6}}})

u = W (- \frac{1}{6 e ^{\frac{7 x}{6}}})

Substitute back

u = - y - \frac{7}{6} x,

solve for

y

Solve

- y - \frac{7}{6} x = W (- \frac{1}{6 e ^{\frac{7 x}{6}}}) : y = - \frac{6 W ( - \frac{1}{6 e ^{\frac{7 x}{6}}} ) + 7 x}{6}

y = - \frac{6 W ( - \frac{1}{6 e ^{\frac{7 x}{6}}} ) + 7 x}{6}

2^{20 x + 10} = 3 2^{3 x + 6}

(0.5)^{- 25 6^{4^{x}}} = 4

5^{3 x + 2} = 1 1^{7 x - 2}

\frac{4 ^{x - 1}}{2 ^{x + 2}} = 256

2 7^{- x - 1} = 81

What is the answer to solvefor y,7x+6y=e^y ?
The answer to solvefor y,7x+6y=e^y is y=-(6\W(-1/(6e^{\frac{7x){6}}})+7x)/6