Question

If $x>1,y>1,z>1$ are in G.P, then $\frac{1}{1+lnx},\frac{1}{1+lny},\frac{1}{1+lnz}$ are in

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

Answer 1

The correct option is B H.P

Given $x,y,z$ are in G.P
$\Rightarrow \ln {\left(y\right)}^2=\ln \left(xz\right)$
$\Rightarrow 2\ln y=\ln x+\ln z$
$\Rightarrow 2(1+\ln y)=(1+\ln x)+(1+\ln z)$
$\Rightarrow 1+\ln x,1+\ln y,1+\ln z$ are in A.P
$\Rightarrow \frac{1}{1+\ln x},\frac{1}{1+\ln y},\frac{1}{1+\ln z}$ are in H.P