The solution set of the inequality ${\rm{lo}}{{\rm{g}}_{{\rm{sin}}\left( {\frac{\pi }{3}} \right)}}\left( {{x^2} - 3x + 2} \right) \ge 2$ is

$\left( {\frac{1}{2},2} \right)$

$\left( {1,\frac{5}{2}} \right)$

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

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Application +4 | -1

The solution set of the inequality

\mathrm{lo}{\mathrm{g}_{\mathrm{sin}\left( {\frac{\pi }{3}} \right)}}\left( {{x^2} - 3x + 2} \right) \ge 2

View answer and explanation

Correct option: C

\left[ {\left. {\frac{1}{2},1} \right) \cup \left( {2,\frac{5}{2}} \right.} \right]

Option C

\left[ {\left. {\frac{1}{2},1} \right) \cup \left( {2,\frac{5}{2}} \right.} \right]

is correct because it represents the intersection of the solution set of the logarithmic inequality and the domain of the logarithm.