make x the subject of the formula; a^x +bx+c=0


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 165226 by Neils last updated on 27/Jan/22

$m a k e x t h e s u b j e c t o f t h e f o r m u l a;$ $a^{x} + b x + c = 0$
	Answered by mr W last updated on 28/Jan/22

	$a^{x} = - (b x + c)$ ${(a^{\frac{1}{b}})}^{b x} = - (b x + c)$ ${(a^{\frac{1}{b}})}^{b x + c} = - (b x + c) a^{\frac{c}{b}}$ $e^{(b x + c) \frac{\ln a}{b}} = - (b x + c) a^{\frac{c}{b}}$ $- (b x + c) \frac{\ln a}{b} e^{- (b x + c) \frac{\ln a}{b}} = \frac{\ln a}{{b a}^{\frac{c}{b}}}$ $- (b x + c) \frac{\ln a}{b} = W (\frac{\ln a}{{b a}^{\frac{c}{b}}})$ $\Rightarrow x = - \frac{c}{b} - \frac{1}{\ln a} W (\frac{\ln a}{{b a}^{\frac{c}{b}}})$
	Commented by Neils last updated on 27/Jan/22

	$A v e r y n i c e s o l u t i o n b u t {t h e r e}^{'} s a s l i g h t m i s t a k e f r o m t h e f i f t h l i n e$ $Y o u o m i t t e d a m i n u s s i g n$
	Commented by mr W last updated on 28/Jan/22

	$t h a n k s s i r!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum