solve-using-LambertW-function-8-7-x-17-25x-

Question Number 120154 by mathace last updated on 29/Oct/20

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

{(\frac{8}{7})}^{x} + 17 = 25 x

Answered by mr W last updated on 29/Oct/20

{(\frac{8}{7})}^{x} = 25 (x - \frac{17}{25})

{(\frac{8}{7})}^{x - \frac{17}{25}} = 25 {(\frac{8}{7})}^{- \frac{17}{25}} (x - \frac{17}{25})

e^{(x - \frac{17}{25}) \ln \frac{8}{7}} = 25 {(\frac{8}{7})}^{- \frac{17}{25}} (x - \frac{17}{25})

- \frac{1}{25} {(\frac{8}{7})}^{\frac{17}{25}} \ln \frac{8}{7} = (\frac{17}{25} - x) (\ln \frac{8}{7}) e^{(\frac{17}{25} - x) \ln \frac{8}{7}}

W [- \frac{1}{25} {(\frac{8}{7})}^{\frac{17}{25}} \ln \frac{8}{7}] = (\frac{17}{25} - x) \ln \frac{8}{7}

\Rightarrow x = \frac{17}{25} - \frac{1}{\ln \frac{8}{7}} W [- \frac{1}{25} {(\frac{8}{7})}^{\frac{17}{25}} \ln \frac{8}{7}]

\approx {\begin{cases} 0.724057 \\ 53.864856 \end{cases}

Commented by mathace last updated on 30/Oct/20

C o r r e c t! T h a n k y o u s i r .

Commented by mathace last updated on 30/Oct/20

W o u l d y o u p l z h e l p t o s o l v e t h e f o l l o w i n g

b y L a m b e r t W o r o t h e r s p a c i a l f u n c t i o n

{(\frac{8}{7})}^{x} + 17^{x} = 25 x

Commented by mr W last updated on 30/Oct/20

n o c h a n c e!

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