Solve-for-x-in-4-x-192-x-Using-lambert-function-

Question Number 6870 by Tawakalitu. last updated on 31/Jul/16

S o l v e f o r x i n

4^{x} = \frac{192}{x}

U s i n g l a m b e r t f u n c t i o n

Commented by Yozzii last updated on 31/Jul/16

a^{b x + c} = \frac{d}{f x + g} (a, b, c, d, f, g \in R, a \neq 1, d \neq 0, f \neq 0, b \neq 0, a > 0)

\Rightarrow (f x + g) e^{(b x + c) l n a} = d

(f \frac{b l n a}{b l n a} x + g) e^{c l n a} e^{b x l n a} = d

\frac{{f e}^{c l n a - \frac{g b l n a}{f}}}{b l n a} (b x l n a + \frac{g b l n a}{f}) e^{b x l n a + \frac{g b l n a}{f}} = d

b x l n a + \frac{g b l n a}{f} = W {\frac{d b l n a}{f} e^{\frac{g b l n a}{f} - c l n a}}

x = \frac{1}{b l n a} [W {\frac{d b l n a}{f} e^{\frac{g b l n a}{f} - c l n a}} - \frac{g b l n a}{f}]

e = {E u l e r}^{'} s c o n s t a n t

I n y o u r p r o b l e m, b = f = 1, c = g = 0, d = 192, a = 4

\Rightarrow x = \frac{1}{l n 4} W {192 l n 4}

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