solve for x (1+(1/x))^(x+1) =(1+(1/6))^6 show working


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Question Number 176189 by Linton last updated on 14/Sep/22

$s o l v e f o r x$ ${(1 + \frac{1}{x})}^{x + 1} = {(1 + \frac{1}{6})}^{6}$ $s h o w w o r k i n g$
	Answered by BaliramKumar last updated on 14/Sep/22

	${(\frac{x + 1}{x})}^{x + 1} = {(1 + \frac{1}{6})}^{6}$ ${(\frac{x}{x + 1})}^{- (x + 1)} = {(1 + \frac{1}{6})}^{6}$ ${(\frac{x + 1 - 1}{x + 1})}^{- (x + 1)} = {(1 + \frac{1}{6})}^{6}$ ${(1 - \frac{1}{x + 1})}^{- (x + 1)} = {(1 + \frac{1}{6})}^{6}$ $p u t - (x + 1) = y$ ${(1 + \frac{1}{y})}^{y} = {(1 + \frac{1}{6})}^{6}$ $y = 6$ $- (x + 1) = 6$ $x + 1 = - 6$ $x = - 7 Answer$
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