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

• A

  $(2, \infty)$
• Correct answer
  B

  $(2,3) \cup(4, \infty)$
• C

  $(4,5) \cup(5, \infty)$
• D

  $(2,3) \cup(4,5)$

Solution

Clearly $x>2$. Write the given inequality
as
$\begin{aligned}<br />& \left(x^2-6 x+8\right) \log (x-2)>0 \Leftrightarrow(x-2)(x-4) \log (x-2)> \\<br />& 0 \\<br />& \Leftrightarrow(x-4) \log (x-2)>0 \quad[\therefore x>2]<br />\end{aligned}$

Hence, the correct answer is option: 'B'.