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If `(log)_3{5+4(log)_3(x-1)}=2,`then `x`is equal to4 (b) 3(c) 8 (d) `(log)_2 16`A. 2B. 4C. 8D. 16 |
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Answer» Correct Answer - B 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` |
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