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Q. \( \frac{3^{2x-8}}{225} = \frac{5^3}{5^x} \)
(a) 2 (b) 3 (c) 5 (d) 4
✏️ Solution
\( 225 = 3^2 \cdot 5^2 \)
\( \frac{3^{2x-8}}{3^2 \cdot 5^2} = 5^{3-x} \)
\( 3^{2x-10} \cdot 5^{-2} = 5^{3-x} \)
\( 3^{2x-10} = 5^{5-x} \)
Since bases differ, both sides must be constants ⇒ match exponents:
\( 2x – 10 = 0 \Rightarrow x = 5 \)
Correct Option: (c) 5
\( \boxed{5} \)