Given p<x<q is solution set inequality 1+2^x +2^(2x) +2^(3x) +...>2 for x≠1. find the value of 5p−3q .


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Question Number 142968 by bramlexs22 last updated on 08/Jun/21

$G i v e n p < x < q i s s o l u t i o n s e t$ $i n e q u a l i t y 1 + 2^{x} + 2^{2 x} + 2^{3 x} + . . . > 2$ $f o r x \neq 1 . f i n d t h e v a l u e o f$ $5 p - 3 q .$
	Answered by mr W last updated on 08/Jun/21

	$- 1 < 2^{x} < 1 \Rightarrow x < 0$ $\frac{1}{1 - 2^{x}} > 2 \Rightarrow 2^{x} > 2^{- 1} \Rightarrow x > - 1$ $\Rightarrow - 1 < x < 0$ $i . e . p = - 1, q = 0$ $5 p - 3 q = - 5$
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