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Q. \( \frac{1}{243^x} = 729^y = 3^3 \)
✏️ Solution
\( 243 = 3^5,\quad 729 = 3^6 \)
\( \frac{1}{243^x} = (3^5)^{-x} = 3^{-5x} \)
\( 729^y = (3^6)^y = 3^{6y} \)
\( 3^{-5x} = 3^3 \Rightarrow -5x = 3 \)
\( x = -\frac{3}{5} \)
\( 3^{6y} = 3^3 \Rightarrow 6y = 3 \)
\( y = \frac{1}{2} \)
\( \boxed{x = -\frac{3}{5},\ y = \frac{1}{2}} \)