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If S={x in R :((log)(0. 6)0. 216)(log)5...

If `S={x in R :((log)_(0. 6)0. 216)(log)_5(5-2x)lt=0},` then `S` is equal to `(2. 5 ,oo)` (b) `(2, 2.5)` (c) `(2, 2.5)` (d) `(0, 2.5)`

A

`[ 2.5, infty)`

B

` [2, 2.5)`

C

` (2, 2.5)`

D

`(0, 2.5)`

Text Solution

Verified by Experts

The correct Answer is:
B
` ( log_((0.6))(0.6)^(3)) log_(5) (5-2x) le 0`
` rArr 5 - 2x le 1 `
` rArr x ge 2 ` ...(i)
Also`, 5 - 2x gt 0` ...(ii)
From Eqs. (i) and (ii), we have ` x in [2, 2.5)`.
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