Question

If 3 numbers a,b,c are in G.P., then $loga,logb,logc$ are in:

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

Answer 1

The correct option is A

A.P

The three numbers a,b and c are in G.P., then

$b^2$ = ac

Applying Log on both sides,

$log{b}^2=log\left(ac\right)$

$\Rightarrow 2lo{g}_{10}b$ = $lo{g}_{10}a+lo{g}_{10}c$ (When three terms are in an A.P, Sum of the first and the third term is equal to twice the second term.)

Thus, $loga,logb,logc$ are in AP