5×6^x −3×4^x = 2×9^x I need an explanation.


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Question Number 53827 by Mikael_Marshall last updated on 26/Jan/19

$5 \times 6^{x} - 3 \times 4^{x} = 2 \times 9^{x}$ $I n e e d a n e x p l a n a t i o n .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19

	$5 \times 3^{x} \times 2^{x} - 3 \times 2^{x} \times 2^{x} = 2 \times 3^{x} \times 3^{x}$ $a = 2^{x} b = 3^{x}$ $5 a b - 3 a^{2} = 2 b^{2}$ $3 a^{2} - 5 a b + 2 b^{2} = 0$ $3 a^{2} - 3 a b - 2 a b + 2 b^{2} = 0$ $3 a (a - b) - 2 b (a - b) = 0$ $(a - b) (3 a - 2 b) = 0$ $e i t h e r a - b = 0$ $a = b$ $2^{x} = 3^{x}$ ${(\frac{2}{3})}^{x} = 1 = {(\frac{2}{3})}^{0} s o x = 0$ $o r w h e n$ $3 a - 2 b = 0$ $3 \times 2^{x} = 2 \times 3^{x}$ $\frac{2^{x}}{3^{x}} = \frac{2}{3}$ ${(\frac{2}{3})}^{x} = {(\frac{2}{3})}^{1} s o x = 1$ $h e n c e x i s e i t h e r 0 o r 1$
	Commented by Mikael_Marshall last updated on 26/Jan/19

	$t h a n k y o u b r o$
	Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19

	$m o s t w e l c o m e . . .$
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