The set of real values of $x$ for which the inequality $\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}$ holds is

Question and options

The set of real values of

x

for which the inequality

\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}

holds is

Correct answer: A - $[2,81)$

log27 8 = log3 2, so x>=2. 9^(1/log2 3)=9^(log3 2)=3^(2log3 2)=4, so log3 x<4 gives x<81. Set [2,81).