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Q. If \( 4^x – 4^{x-1} = 24 \), find \( (2x)^x \)
(a) \( 5\sqrt{5} \) (b) \( \sqrt{5} \) (c) \( 25\sqrt{5} \) (d) 125
✏️ Solution
\( 4^x – 4^{x-1} = 24 \)
\( = 4^{x-1}(4 – 1) = 24 \)
\( 3 \cdot 4^{x-1} = 24 \)
\( 4^{x-1} = 8 = 2^3 \)
\( (2^2)^{x-1} = 2^3 \Rightarrow 2x – 2 = 3 \)
\( x = \frac{5}{2} \)
\( (2x)^x = (5)^{5/2} \)
\( = 5^2 \cdot \sqrt{5} = 25\sqrt{5} \)
Correct Option: (c) \( 25\sqrt{5} \)
\( \boxed{25\sqrt{5}} \)