Q106 / 160 · WBJEE 2009 · Mathematics

If $a, b, c$ are in G.P. $(a>1, b>1, c>1)$, then for any real number $x($ with $x>0, x \neq 1), \log _{\mathrm{a}} x, \log _{\mathrm{b}} x, \log _{\mathrm{c}} x$ are in

  • A
    G.P.
  • B
    A.P.
  • Correct answer
    C
    H.P.
  • D
    G.P. but not in H.P.

Solution

Hints : $a, b, c$ are in G.P. $\Rightarrow \log _x a, \log _x b, \log _x c$ are in A.P. $\Rightarrow \frac{1}{\log _x a}, \frac{1}{\log _x b}, \frac{1}{\log _x c}$ arein H.P. $\Rightarrow \log _a X, \log _b X, \log _c X$ are in H.P.

Hence, the correct answer is option: 'C'.

Relevant Questions