If `(log)_3{5+4(log)_3(x-1)}=2,` then `x` is equal to 4 (b) 3 (c) 8 (d) `(log)_2 16`

Options

A. 2
B. 4
C. 8
D. 16

Answer

B

Explanation

We must have ` x - 1 gt 0`
` rArr x gt 1`…(i)
` and 5+4 log_(3) (x-1) gt 0`
` or 4 log_(3) (x-1) gt - 5`
` or log_(3) (x-1) gt - 5/4`
` or x - 1 gt 3^(-5//4)`
` or x gt 1+3^(-5//4)` …(ii)
From Eqs. (i) and (ii), we get ` x gt 1 + 3^(-5//4)`
`:. 5+4 log_(3) (x-1) = 9`
` rArr 4 log_(3) (x-1) = 4`
` or log_(3) (x-1) = 1`
` or x -1 = 3 or x = 4`