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If agt1,bgt1andcgt1 are in G.P., then sh...

If `agt1,bgt1andcgt1` are in G.P., then show that `1/(1+log_(e)a),1/(1+log_(e)b)and1/(1+log_(e)c)` are in H.P.

Text Solution

Verified by Experts

It is given that a,b,c are in G.P. Hence,
`b^(2)=ac`
or `2log_(e)b=log_(e)a+log_(e)c`
Hence, `log_(e)a,log_(e)b,andlog_(e)c` are in A.P.
`rArr1+log_(e)a,1+log_(e)b,and1+log_(e)c` are in A.P.
`rArr1/(1+log_(e)a),1/(1+log_(e)b),1/(1+log_(e)c)` are in H.P.
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