Solve for x. 3^(2x) = 18x please i need workings.


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Question Number 10317 by Tawakalitu ayo mi last updated on 03/Feb/17

$Solve for x .$ $3^{2 x} = 18 x$ $please i need workings .$
	Answered by mrW1 last updated on 03/Feb/17
	$(3^2 )^x =18x 9^x =18x e^(xln 9) =18x 1=((18)/(−ln 9))(−xln 9)e^(−xln 9) (−xln 9)e^(−xln 9) =−((ln 9)/(18)) −xln 9=W(−((ln 9)/(18))) with W=Lambert W function x=−((W(−((ln 9)/(18))))/(ln 9))=−((W(−0.122068))/(2.197225)) = { ((−((−0.140479)/(2.197225))=0.063935)),((−((−3.295837)/(2.197225))=1.5)) :}$
	${(3^{2})}^{x} = 18 x$ $9^{x} = 18 x$ $e^{x \ln 9} = 18 x$ $1 = \frac{18}{- \ln 9} (- x \ln 9) e^{- x \ln 9}$ $(- x \ln 9) e^{- x \ln 9} = - \frac{\ln 9}{18}$ $- x \ln 9 = W (- \frac{\ln 9}{18}) w i t h W = L a m b e r t W f u n c t i o n$ $x = - \frac{W (- \frac{\ln 9}{18})}{\ln 9} = - \frac{W (- 0.122068)}{2.197225}$ $= {\begin{cases} - \frac{- 0.140479}{2.197225} = 0.063935 \\ - \frac{- 3.295837}{2.197225} = 1.5 \end{cases}$
	Commented by Tawakalitu ayo mi last updated on 04/Feb/17

	$God bless you sir .$
	Answered by arge last updated on 04/Feb/17

	$l o g 3^{2 x} = l o g 18 x$ $2 x l o g 3 = l o g 18 + l o g x$ $l o g x = y$ $0.95 x = 1.26 + y$ $x = \frac{1.26 + y}{0.95}$
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