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If "log"(3) a xx "log"(a) x = 4, then x ...

If `"log"_(3) a xx "log"_(a) x = 4`, then x is equal to

A

`(1)/(2x+ 1)`

B

`(1)/(2y+ 1)`

C

2xy +1

D

`(1)/(2xy-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`"log"_(4) 5 =x " and "log"_(5) 6 =y`
`rArr 5 = 4^(x) " and " 6 =5^(y)`
`rArr 6 =(4^(x))^(y)`
`rArr 6 =4^(xy)`
`rArr 2 xx 3 = 2^(xy) rArr 3 = 2^(2xy-1) rArr 3^((1)/(2xy-1)) = 2`
`rArr "log"_(3) 2 = (1)/(2xy-1)`
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