find the value of x if 3^x = 9x


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Question Number 38488 by Rio Mike last updated on 26/Jun/18

$find the value of x if$ $3^{x} = 9 x$
	Answered by $@ty@m last updated on 26/Jun/18

	$3$
	Answered by MrW3 last updated on 26/Jun/18
	$e^(xln 3) =9x 1=9xe^(−xln 3) −(1/9)=−xe^(−xln 3) −((ln 3)/9)=(−xln 3)e^(−xln 3) ⇒−xln 3=W(−((ln 3)/9)) ⇒x=−((W(−((ln 3)/9)))/(ln 3))= { ((−((−0.1405)/(ln 3))=0.1279)),((−((−3.2958)/(ln 3))=3)) :}$
	$e^{x \ln 3} = 9 x$ $1 = 9 {x e}^{- x \ln 3}$ $- \frac{1}{9} = - {x e}^{- x \ln 3}$ $- \frac{\ln 3}{9} = (- x \ln 3) e^{- x \ln 3}$ $\Rightarrow - x \ln 3 = W (- \frac{\ln 3}{9})$ $\Rightarrow x = - \frac{W (- \frac{\ln 3}{9})}{\ln 3} = {\begin{cases} - \frac{- 0.1405}{\ln 3} = 0.1279 \\ - \frac{- 3.2958}{\ln 3} = 3 \end{cases}$
	Commented by tawa tawa last updated on 26/Jun/18

	$longest time sir Mrw$
	Commented by MrW3 last updated on 26/Jun/18

	$Y e s, b u t n o w I^{'} m b a c k .$
	Commented by Rio Mike last updated on 26/Jun/18

	$w e l c o m e s i r$
	Commented by MrW3 last updated on 27/Jun/18

	$t h a n k y o u!$
	Commented by tawa tawa last updated on 28/Jun/18

	$welcome back sir .$
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