Question

If $\frac{1}{abc+\log a},\frac{1}{abc+\log b}$ and $\frac{1}{abc+\log c}$, are in H.P, where $a,b,c\in R^{+}$, then $a,b$ and $c$ are in

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

Answer 1

The correct option is B G.P.

$\frac{1}{abc+\log a},\frac{1}{abc+\log b},\frac{1}{abc+\log c}$ are in H.P.
$\Rightarrow abc+\log a,abc+\log b,abc+\log c$ are in A.P.
$\Rightarrow 2(abc+\log b)=(abc+\log a)+(abc+\log c)$
$\Rightarrow 2\log b=\log a+\log c$
$\Rightarrow \log b^2=\log ac\Rightarrow b^2=ac$

Hence $a,b$ and $c$ are in G.P.