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})

6^{2 x} - 34 (6^{x}) - 72 = 0

x, y = A e^{- k x}

2 7^{2 t + 1} = (\frac{1}{9})^{t - 1}

5^{x + 2} = 4^{2 x - 1}

5^{x + 2} = 4^{2 x - 2}

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))