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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Sequence and Series
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$a^x=b^y=c^z=d^t$ and $a, b, c, d$ are in GP, then $x, y, z, t$ are in


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Answer : (c) HP
Explanation : a , b , c , d are in GP
$x\;log a=y\; log b=z\;log c=t\;log d$
$\large\frac{x}{y}=\large\frac{log b}{log a}=\large\frac{log a_{r}}{log a}$
$\large\frac{x}{y}=\large\frac{log a+log r}{log a}$
Similarly , $\large\frac{x}{z}=1+2\;\large\frac{log\;r}{log\;a}----(2)$
From $\;(1)\;and\;(2)$
From $(1)\;,(2)\;and\;(3)$
$From (4) \;and\;(5)\;$x , y , z , t are in HP.
answered Jan 24, 2014 by yamini.v

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