What is the answer to -3.73=-4xe^{-x/4} ?

The answer to -3.73=-4xe^{-x/4} is x=-4\W_{-1}(-(3.73)/(16)),x=-4\W_{0}(-(3.73)/(16))

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-3.73=-4xe^{-x/4}

- 3.73 = - 4 x e^{- \frac{x}{4}}

x = - 4 W_{- 1} (- \frac{3.73}{16}), x = - 4 W_{0} (- \frac{3.73}{16})

Decimal Notation

x = 9.12253 \dots, x = 1.28614 \dots

Solution steps

- 3.73 = - 4 x e^{- \frac{x}{4}}

Rewrite the equation with

- \frac{x}{4} = u

and

x = - 4 u

- 3.73 = - 4 (- 4 u) e^{u}

Rewrite

- 3.73 = - 4 (- 4 u) e^{u}

in Lambert form:

e^{u} u = - \frac{3.73}{16}

Solve

e^{u} u = - \frac{3.73}{16} : u = W_{- 1} (- \frac{3.73}{16}), u = W_{0} (- \frac{3.73}{16})

u = W_{- 1} (- \frac{3.73}{16}), u = W_{0} (- \frac{3.73}{16})

Substitute back

u = - \frac{x}{4},

solve for

x

Solve

- \frac{x}{4} = W_{- 1} (- \frac{3.73}{16}) : x = - 4 W_{- 1} (- \frac{3.73}{16})

Solve

- \frac{x}{4} = W_{0} (- \frac{3.73}{16}) : x = - 4 W_{0} (- \frac{3.73}{16})

x = - 4 W_{- 1} (- \frac{3.73}{16}), x = - 4 W_{0} (- \frac{3.73}{16})

(4^{n} \cdot 4^{5})^{3} = 4^{27}

9^{x - 5} = 27

(- 0.1 b) e^{- b (- 6.7416)} = 0.86083

3^{2 x + 1} = 9^{x - 1}

1 = e^{x (0.5)}

What is the answer to -3.73=-4xe^{-x/4} ?
The answer to -3.73=-4xe^{-x/4} is x=-4\W_{-1}(-(3.73)/(16)),x=-4\W_{0}(-(3.73)/(16))