InterviewSolution
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InterviewSolution
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`log_(4) 18 ` isA. a rational numberB. an irrational numberC. a prime numberD. none of these |
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Answer» Correct Answer - B Let ` log_(4) 18 = p//q," where "p,q in I` ` rArr log_(4) 9+log_(4) 2 = p/q` ` rArr 1/2 xx 2 log _(2) 3 + 1/2 = p/q` `rArr log_(2) 3 = p/q - 1/2 = m/n(say)` where m, n` in I and n ne 0` ` rArr 3 = (2) ^(m//n)` ` or 3^(n) = 2^(m) ` (possible when m=n = 0 which is not true) Hence, ` log_(4) 18` is an irrational number. |
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