Question

If $x>1,y>1,z>1$ are in G.P. Then $\frac{1}{1+\ln x},\frac{1}{1+\ln y},\frac{1}{1+\ln z}$ are in:

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

Answer 1

The correct option is A A.P.

$x_1,y_1,z\to G\cdot Y$

$y^2=x\times z$

taking log both sides

$\ln y^2=\ln (x\times z)$

$2\ln y=\ln x+\ln z$

$2(1+\ln y)=(1+\ln x)+(1+\ln z)$

$\therefore 1+\ln x,1+\ln y,1+\ln z$ are in $AP$

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