If y=a^(1/(1-(log)a x))a n dz=a^(1/(1-(l...

If `y=a^(1/(1-(log)_a x))a n dz=a^(1/(1-(log)_a y)),t h e np rov et h a tx=a^(1/(1-(log)_a z))`

A

`(1)/(a^(1-"log"az))`

B

`(1)/(1-"log"_(a)z)`

C

`(1)/(1+"log"_(z)a)`

D

`(1)/(1-"log"_(z)a)`

Text Solution

Verified by Experts

The correct Answer is:

B

We have,
`y= a^((1)/(1-"log"_(a)z)) " and " z= a^((1)/(1-"log"_(a)y))`
`rArr "log"_(a)y= (1)/(1-"log"_(a)x) " and log"_(a) z = (1)/(1-"log"_(a)y)`
`rArr "log"_(a)x= ("log"_(a)y-1)/("log"_(a)y) " and "1-"log"_(a)z = ("log"_(a)y)/("log"_(a)y-1)`
`rArr "log"_(a)x= (1)/(1-"log"_(a)z)`
`rArr k = (1)/(1-"log"_(a)z) " " [because x = a^(k) therefore "log"_(a)x = k]`

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