If _a x, ; _b x, ; _c x be in H.P., then a, ;b, ;c are in - Vidyadip

MCQ

If ${\log _a}x,\;{\log _b}x,\;{\log _c}x$ be in $H.P.$, then $a,\;b,\;c$ are in

A
$A.P.$
B
$H.P.$
✓
$G.P.$
D
None of these

✓

Answer

Correct option: C.

$G.P.$

c
(c) Here $\frac{{\log x}}{{\log a}},\;\frac{{\log x}}{{\log b}},\;\frac{{\log x}}{{\log c}}$ are in $H.P.$

$ \Rightarrow $$\frac{{\log a}}{{\log x}},\;\frac{{\log b}}{{\log x}},\;\frac{{\log c}}{{\log x}}$ are in $A.P.$

$ \Rightarrow $${\log _x}a,\;{\log _x}b,\;{\log _x}c$ are in $A.P.$

$ \Rightarrow $$a,\;b,\;c$ are in $G.P.$

Note : Students should remember this question as a fact.

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