Question

${\log }_{3}2,{\log }_{6}2,{\log }_{12}2$ are in-

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

Answer 1

The correct option is C H.P.

If the given numbers represented by $x,y,z$ then
$\frac{1}{x}={\log }_{2}3,\frac{1}{y}={\log }_2(2\times 3)=1+{\log }_{2}3,$

$\frac{1}{z}={\log }_2(4\times 3)=2+{\log }_{2}3$ which are in A.P.

$\therefore$ $x,y,z$ are in H.P.