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If "log"(a) x xx "log"(5)a = "log"(x) 5,...

If `"log"_(a) x xx "log"_(5)a = "log"_(x) 5, a ne 1, a gt 0, " then "x =`

A

a

B

`5, (1)/(5)`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`"log"_(a) x xx "log"_(5)a = "log"_(x)5`
`rArr "log"_(5) x= "log"_(x) 5`
`rArr "log"_(5)x = (1)/("log"_(5)x)`
`rArr ("log"_(5)x)^(2) = 1 rArr "log"_(5)x = +-1 rArr x = 5^(+-1) rArr x = 5, (1)/(5)`
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