solve-for-x-by-using-lambert-function-2-x-3x-8-

Question Number 183825 by Michaelfaraday last updated on 30/Dec/22

s o l v e f o r x b y u s i n g l a m b e r t f u n c t i o n

2^{x} + 3 x = 8

Answered by MJS_new last updated on 30/Dec/22

generally

b^{x} = a x + c

inserting x = - \frac{t}{\ln b} - \frac{c}{a} and transforming leads to

e^{t} t = - \frac{\ln b}{b^{c / a} a}

\Rightarrow x = - \frac{c}{a} - \frac{1}{\ln b} W (- \frac{\ln b}{b^{c / a} a})

Commented by Michaelfaraday last updated on 30/Dec/22

t h a n k s s i r

Commented by MJS_new last updated on 31/Dec/22

{you}^{'} re welcome

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