8x=16^x x=?


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Question Number 121850 by Khalmohmmad last updated on 12/Nov/20

$8 x = 16^{x}$ $x = ?$
	Answered by mr W last updated on 12/Nov/20
	$8x=e^(xln 16) 8x×e^(−xln 16) =1 (−xln 16)×e^(−xln 16) =−((ln 16)/8)=−((ln 2)/2) −x ln 16=W(−((ln 2)/2)) ⇒x=−(1/(4ln 2))W(−((ln 2)/2))= { ((1/2)),((1/4)) :}$
	$8 x = e^{x \ln 16}$ $8 x \times e^{- x \ln 16} = 1$ $(- x \ln 16) \times e^{- x \ln 16} = - \frac{\ln 16}{8} = - \frac{\ln 2}{2}$ $- x \ln 16 = W (- \frac{\ln 2}{2})$ $\Rightarrow x = - \frac{1}{4 \ln 2} W (- \frac{\ln 2}{2}) = {\begin{cases} \frac{1}{2} \\ \frac{1}{4} \end{cases}$
	Commented by BeeMee last updated on 12/Nov/20

	$d o n t u n d e r s t a n d t h e t h i r d l i n e p l e a s e$
	Commented by mr W last updated on 12/Nov/20

	$8 x \times e^{- x \ln 16} = 1$ $x \times e^{- x \ln 16} = \frac{1}{8}$ $(- x \ln 16) \times e^{- x \ln 16} = - \frac{\ln 16}{8}$ $(- x \ln 16) \times e^{- x \ln 16} = - \frac{\ln 2}{2}$ $- x \ln 16 = W (- \frac{\ln 2}{2})$ $. . .$
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