If 4x – 4x-1 = 24, then (2x)x equals A. \(5\sqrt5\)B. \(\sqrt5\)C

1.	If 4x – 4x-1 = 24, then (2x)x equals A. \(5\sqrt5\)B. \(\sqrt5\)C. \(25\sqrt5\)D. 125
Answer» 4^x – 4^{x – 1} = 24 Let 4x = y y - \(\frac{y}4\)= 24 4y – y = 96 y = 32 4^x = 32 2^2x = 2⁵ (2x)^x = \((2\times\frac{5}{2})^{\frac{5}{2}}\) (5)^5/2= \(25\sqrt5\)

If 4x – 4x-1 = 24, then (2x)x equals A. \(5\sqrt5\)B. \(\sqrt5\)C. \(25\sqrt5\)D. 125

Answer»

4^x – 4^{x – 1} = 24

Let 4x = y

y - \(\frac{y}4\)= 24

4y – y = 96

y = 32

4^x = 32

2^2x = 2⁵

(2x)^x = \((2\times\frac{5}{2})^{\frac{5}{2}}\)

(5)^5/2= \(25\sqrt5\)