loga \((\frac{3}{2})\) = \( - \frac{1}{2}\) হলে, x -এর মান কত ?

log_a \((\frac{3}{2})\) = \( - \frac{1}{2}\) হলে, x -এর মান কত ?

A \(\frac{4}{9}\)

B \(\frac{9}{4}\)

C \(\sqrt {\frac{3}{2}} \)

D \(\sqrt {\frac{2}{3}} \)

Correct Answer: Option A

log_x \((\frac{3}{2})\) = -\(\frac{1}{2}\) = x^{\(\frac{1}{2}\)} =\(\frac{3}{2}\) =\(\frac{1}{{{x^{\frac{1}{2}}}}}\) =\(\frac{3}{2}\)

=\(\frac{1}{{\sqrt x }}\) =\(\frac{3}{2}\) =\(\sqrt x \) =\(\frac{2}{3}\) =x =\((\frac{2}{3})\)² x = \(\frac{4}{9}\)