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Q)

If $x>1,y>1,z>1$ are in G.P then $\large\frac{1}{1+ln\; x},\frac{1}{1+ln\; y},\frac{1}{1+ln \;z}$ are in

$(a)\;A.P\qquad(b)\;G.P\qquad(c)\;H.P\qquad(d)\;None\;of\;these$

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A)
$x,y,z$ are in G.P
$\large\frac{y}{x}=\frac{z}{y}=$$\log _e\big(\large\frac{y}{x}\big)=$$\log_e\big(\large\frac{z}{y}\big)$
$ln \;y-ln \;x=ln\; z-ln\; y$
$ln\;x,ln\; y,ln \;z$ are in A.P
$\large\frac{1}{1+ln\;x}.\frac{1}{1+ln\;y}.\frac{1}{1+ln\;z}$ are in H.P
Hence (c) is the correct answer.
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