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If x gt 1 , y gt 1 , z gt 1 are in G.P. ...

If `x gt 1 , y gt 1 , z gt 1` are in G.P. , then `(1)/(1 + log x) , (1)/(1 + log y)` and `(1)/(1 + log z)` are in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`:.x,y,z`are in GP `" " " "[x,y,zgt1]`
`:.1nx,1ny,1nz` are in AP.
and `2x,4x,6x` are also in AP. `" " " "[xgt1]`
By property,
`2x+1nx,4x+1ny,6x+1nz` are also in AP.
`(1)/(2x+1nx),(1)/(4x+1ny),(1)/(6x+1nz)` are in HP.
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