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# If three numbers are in GP, then their logarithms will be in

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;None\;of\;the\;above$

Can you answer this question?

Answer : (a) AP
Explanation : a,b,c are in GP $\frac{b}{a}=\frac{c}{b}$
$b^2=ac$
logarithm on both sides
$log\;(b^2)=\;log(ac)$
$2\;log\;b=log\;a+log\;c=log\;b+log\;b$
$log\;b-log\;a=log\;c-log\;b$
Therefore , $log\;a,log\;b,log\;c\;are\;in\;AP.$
answered Jan 17, 2014 by