The solution set of the inequality `(log)_(10)(x^2-16)lt=(log)_(10)(4x-11)` is `4,oo)` (b) `(4,5)` (c) `((11)/4,oo)` (d) `((11)/4,5)`

Options

A. ` (4, infty)`
B. ` (4, 5]`
C. `(11//4, infty)`
D. ` (11/4, 5)`

Answer

B

Explanation

`x^(2) - 16 le 4x - 11`
` rArr x^(2) - 4x - 5 le 0`
` rArr (x-5) (x+1) le 0`
` rArr - 1 le x le 5` …(i)
Also ` x^(2) - 16 gt 0`
` rArr x lt - 4 or x gt 4` …(ii)
` And 4x - 11 gt 0`
` rArr x gt 11//4` ...(iii)
From Eqs. (i),(ii) and (iii), we have ` x in (4, 5]`.