Question

If $x,y$ and $z$ are in geometric progression, then ${\log }_{x}10,{\log }_{y}10,{\log }_{z}10$ are in

• A. Arithmetic progression
• B. Geometric progression
• C. Harmonic progression
• D. None of these

Answer 1

The correct option is C Harmonic progression

Given, $x,y\text{and}z$ are in G.P.

$\Rightarrow y^2=xz$

taking $log$ on both sides, We get

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

also can be written as:

$\frac{2}{lo{g}_{y}10}=\frac{1}{{\log }_{x}10}+\frac{1}{{\log }_{z}10}$

$\therefore {\log }_{x}10,{\log }_{y}10\text{and}{\log }_{z}10$ are in H.P.