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If a >1,b >1a n dc >1 are in G.P. then s...

If `a >1,b >1a n dc >1` are in G.P. then show that `1/(1+(log)_e a),1/(1+(log)_e b), a n d1/(1+(log)_e c)` are in H.P.

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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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