🎥 Watch Video Solution
Q. \( \left(\frac{2}{3}\right)^x \left(\frac{3}{2}\right)^{2x} = \frac{81}{16} \)
(a) 2 (b) 3 (c) 4 (d) 1
✏️ Solution
\( \left(\frac{3}{2}\right)^{2x} = \left(\frac{2}{3}\right)^{-2x} \)
\( \left(\frac{2}{3}\right)^x \cdot \left(\frac{2}{3}\right)^{-2x} = \frac{81}{16} \)
\( \left(\frac{2}{3}\right)^{-x} = \frac{81}{16} \)
\( \left(\frac{3}{2}\right)^x = \frac{81}{16} \)
\( \frac{81}{16} = \frac{3^4}{2^4} = \left(\frac{3}{2}\right)^4 \)
\( x = 4 \)
Correct Option: (c) 4
\( \boxed{4} \)