Question

If a , b , c be three distinct positive real numbers in G.P, then ${\log }_{a}p,{\log }_{b}p,{\log }_{b}p$ will

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

Answer 1

The correct option is C H.P.

a, b, c are in G.P.

$\therefore b^2=a\times c$

on taking log both sides with base p

${\log }_p{b}^2={\log }_p(a\times c)$

$\begin{array}{cc}2{\log }_{p}b& ={\log }_{p}a+{\log }_{p}c\\ \frac{2}{{\log }_{b}P}& =\frac{1}{{\log }_{a}P}+\frac{1}{{\log }_{c}P}\end{array}$

$\therefore {\log }_{a}P,{\log }_{b}P,{\log }_{c}P\text{are in}H\cdot P$