CAT Exam Model Paper 2 with solutions for free online practice

Question : 77 of 100

Marks: +1, -0

If S is the set of all x ∈ R such that

x ^ { ( \log x ) ^ { 2 } - 3 \log x + 1 } > 1000

then S +

Solution:

(b) Taking log on both sides

[ ( \log x ) ^ { 2 } - 3 \log x + 1 ] \log x > \log 10 ^ { 3 }

( \log x ) ^ { 3 } - 3 ( \log x ) ^ { 2 } + \log x - 3 > 0

( \log x ) ^ { 2 } [ \log x - 3 ] + 1 [ \log x - 3 ] > 0

( \log x - 3 ) [ ( \log x ) ^ { 2 } + 1 ] > 0

\log x - 3 > 0

⇒

\log x > 3

⇒

\log x > \log 1000

⇒

x > 1000

∴ (1000 < S < ∞) is the correct answer.

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