Question

If ${\log }_{10}a,{\log }_{10}b,{\log }_{10}c$ are in A.P, then $a,b,c$ must be in

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

Answer 1

The correct option is B G.P

${\log }_{10}b-{\log }_{10}a={\log }_{10}c-{\log }_{10}b$
$\Rightarrow {\log }_{10}\left(\frac{b}{a}\right)={\log }_{10}\left(\frac{c}{b}\right)\Rightarrow \frac{b}{a}=\frac{c}{b}\Rightarrow b^2=ac$
$\therefore$ $a,b,c$ are in G.P