Question

If $x>1,y>1,z>1$ are in G.P., then ${\log }_{ex}e,{\log }_{cy}e,{\log }_{cz}e$ are in

• A. A.P.
• B. H.P.
• C. G.P.
• D. A.G.P.

Answer 1

Answer: (B)

If $x>1,y>1,z>1$ are in G.P.
$\therefore y^2=xz$
$\therefore 2\ln y=\ln x+\ln z$
$\therefore \ln x,\ln y,\ln z\text{ are in A.P. }$
$\therefore 1+\ln x,1+\ln y;1+\ln z\text{ are in A.P. }$
$\therefore \frac{1}{1+\ln x},\frac{1}{1+\ln y},\frac{1}{1+\ln z}$ are in H.P. $\Rightarrow \frac{1}{\ln ex},\frac{1}{\ln \text{ ey }},\frac{1}{\ln ez}$ are in H.P. or ${\log }_{ex}e,{\log }_{cy}e,{\log }_{ez}e$ are in H.P.