Question

If a>0, b>0, c>0 are in G.P., then $lo{g}_{a}x,lo{g}_{b}x,lo{g}_{c}x$ are in

• 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.
$\therefore b^2=ac$
Let $lo{g}_{a}x=n$
$\therefore x=a^n$
Similarly,
$x=b^l$ and
$x=c^m$
$a^n=b^l=c^m=k$(say)
$\Rightarrow a=k^{\frac{1}{n}}b=k^{\frac{1}{l}}c=k^{\frac{1}{n}}$
Substitute the values of a, b, c in $b^2=ac$
$\frac{2}{l}=\frac{1}{n}+\frac{1}{m}$
Hence $\frac{1}{n},\frac{1}{l},\frac{1}{m}$ are in A.P. or n, l, m are in H.P.