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In which of the folloing `m gt n(m, n in R)` ?A. `m (log_(2)5)^(2)` and `n = log_(2)20`B. `m =log_(10)2` and `n = log_(10)3sqrt(10)`C. `m = log_(10)5. log_(10)20` and `n = 1`D. `m = log_(1//2)((1)/(3))` and `n = log_(1//3)((1)/(2))` |
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Answer» Correct Answer - A::D (A) `m - n = (log_(2)5)^(2) - (log_(2)5 + 2)` `= (log_(2)5 - 2)(log_(2)5 + 1) gt 0` `:. m gt n` (B) `2^(3) lt 10` or `2 lt 10^(1//3)` or `log_(10)2 lt log_(10)10^(1//3)` `:. m lt n` (C) `m = log_(10)5.log_(10)20` `= (log_(10)10 - log_(10)2)(log_(10)10 + log_(10)2)` `=(1 - log_(10)2)(1 + log_(10)2)` `=1 - (log_(10)2)^(2)` `lt 1` `:. m lt n` (D) `m = log_(1//2) ((1)/(3)) = log_(2)3` and `n = log_(1//3)((1)/(2)) = log_(3)2` `:. (m)/(n) = (log_(2)3)/(log_(3)2) = (log_(2)3)^(2) gt 1` `:. m gt n` (as `n gt 0)` |
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