Question

If $x,y,z$ all are greater than unity and are in G.P.then $\frac{1}{1+\log x},\frac{1}{1+\log y},\frac{1}{1+\log z}$ are in

• A. $H.P$
• B. $G.P$
• C. $A.P$
• D. None of these

Answer 1

The correct option is A $H.P$

$x,y,z$ are in GP

$\Rightarrow \log x,\log y,\log z$ are in A.P

$\Rightarrow 1+\log x,1+\log y,1+\log z$ are in A.P

$\Rightarrow \frac{1}{1+\log x},\frac{1}{1+\log y},\frac{1}{1+\log z}$ are in H.P.