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Solution set of `x^((log_(10)x)^(2)-3log_(10)x+1)gt 1000` for `x epsilon R` isA. `(10, oo)`B. `(100, oo)`C. `(1000, oo)`D. `(1, oo)` |
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Answer» Correct Answer - C Solution set of `X^((log_(10)xx)^(2)-3log_(10)x+1)` ………… Taking log on both sides base 10 `-[(log_(10)x)^(2) -3log_(10)x+1]log_(10)xgt log_(10)10^(3)` `implies (log_(10)x)^(3) - 3(log_(10)x)^(2)+log_(10)X -3 gt 0` Let `log_(10)X = t` then `t^(3) - 3t^(2)+ t- 3 gt 0` `implies (t^(2)+1)(t-3)gt0` `implies t - 3 gt 0` `implies log_(10)x gt 3 implies x gt 10^(3)` `implies x epsilon(10^(3), oo)` |
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