Question

If a,b,c are in G. P., Prove that:
${\sf {log_{ a}}}{\sf {x,_{}}}{\sf {log_{ b}}}{\sf {x,_{}}}{\sf {log_{ c}}}{\sf {x_{}}} \sf \: are \: in \: H.P$
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Answer 1

Answer:

a,b,c are in G.P. 

b2=ac

⇒logb2=logac

⇒2logb=loga+logc

∴loga,logbandlogcareinA.P.