if a, b and c are positive, find: ((a/b))^(log_(10) c) ×((b/c))^(log_(10) a) ×((c/a))^(log


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Question Number 71134 by Mr. K last updated on 11/Oct/19

$i f a, b a n d c a r e p o s i t i v e, f i n d :$ ${(\frac{a}{b})}^{{l o g}_{10} c} \times {(\frac{b}{c})}^{{l o g}_{10} a} \times {(\frac{c}{a})}^{{l o g}_{10} b}$
	Answered by MJS last updated on 12/Oct/19

	$\log x^{\log y} = \log y \log x = \log y^{\log x} \Rightarrow x^{\log y} = y^{\log x}$ $\Rightarrow answer = 1$
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