User talk:Fardin2709

please help me

lambert function

the equation
 * $$ ~p^{a x + b} = c x + d $$

where
 * $$ p > 0 \text{ and } c,a \neq 0 $$

can be transformed via the substitution
 * $$ -t = a x + \frac{a d}{c} $$

into
 * $$ t p^t = R = -\frac{a}{c} p^{b-\frac{a d}{c}} $$

giving
 * $$ t = \frac{W(R\ln p)}{\ln p} $$

which yields the final solution
 * $$ x = -\frac{W(-\frac{a\ln p}{c}\,p^{b-\frac{a d}{c}})}{a\ln p} - \frac{d}{c} $$

but if
 * $$ d > p^{b} $$

then, function
 * $$ ~p^{a x + b} = c x + d $$

two roots. this
 * $$ x = -\frac{W(-\frac{a\ln p}{c}\,p^{b-\frac{a d}{c}})}{a\ln p} - \frac{d}{c} $$

first root, but where is second root  !!!!!!!!!!!!