Question

If $x>1,y>1,z>1$ are three numbers in GP then
$\frac{1}{1+\ln x}$, $\frac{1}{1+\ln y}$, $\frac{1}{1+\ln z}$ are in

• A. AP
• B. HP
• C. GP
• D. none of these

Answer 1

The correct option is B HP

Given $y^2=xz$

$\Rightarrow 2lny=lnx+lnz$

$\therefore lnx,lny,lnz$ are in AP

$\Rightarrow lnx+1,lny+1,lnz+1$ are in AP

$\Rightarrow \frac{1}{lnx+1},\frac{1}{lny+1},\frac{1}{lnz+1}$ are in HP