Q. $\log_{2}{\left( x^{2} - 3x + 18 \right) < 4,}$then$\ x$ belongs to
A) (1, 2)
B) (2, 16)
C) (1, 16)
D) None of these
Explanation
(a)
$\log_{2}{\left( x^{2} - 3x + 18 \right) < 4}$
$\Rightarrow x^{2} - 3x + 18 < 16\ \ \ \ ($If$\log_{a}{b < c \Rightarrow b < a^{c})}$
$\Rightarrow x^{2} - 3x + 2 < 0$
$\Rightarrow (x - 1)(x - 2) < 0$
$\Rightarrow x \in (1,\ 2)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.