Solution set of `x^((log_(10)x)^(2)-3log_(10)x+1)gt 1000` for `x epsilon R` is

Options

A. `(10, oo)`
B. `(100, oo)`
C. `(1000, oo)`
D. `(1, oo)`

Answer

C

Explanation

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)`