If {log ₐ}x,{log ₓ}x,{log c}x be in H.P. , then a,b,c are in

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8. Sequences and Series

easy

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

A

$A.P.$

B

$H.P.$

C

$G.P.$

D

None of these

Solution

(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.

Standard 11

Mathematics

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