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BITSAT 2023Paper 2

Exam: BITSAT
Year: 2023
Paper: Paper 2
Subject: Mathematics
Chapter: Basics of Mathematics

BITSAT 2023 · Paper 2 · Mathematics · Basics of Mathematics

The solution set of (x-2)^ x^3-6 x+8 > 1 is

The solution set of

(x-2)^{x^3-6 x+8} > 1

is

The solution set of (x-2)^ x^3-6 x+8 > 1 is

Options

A $(2, \infty)$
B $(2,3) \cup(4, \infty)$
C $(4,5) \cup(5, \infty)$
D $(2,3) \cup(4,5)$

Correct answer

B. $(2,3) \cup(4, \infty)$

Step-by-step solution

Clearly

x > 2

. Write the given inequality
as

\begin{aligned} \\ & \left(x^2-6 x+8\right) \log (x-2) > 0 \Leftrightarrow(x-2)(x-4) \log (x-2) > \\ \\ & 0 \\ \\ & \Leftrightarrow(x-4) \log (x-2) > 0 \quad[\therefore x > 2] \\ \end{aligned}

The solution set of (x-2)^ x^3-6 x+8 > 1 is

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