Question

solve 19 no
give the solution in a page

Answer 1

Here is u r answer...

4X - 4 X-1 = 24
i.e., (2)2x - (2)2(x -1) = 24
i.e., (2)2x - (2)2x -2) = 24
i.e., (2)2x - (2)2x /4= 24

On simplifying, we get
(2)2x = 32 = 25
So, 2x = 5
i.e, x = 5/2
Now,
(2x)x = (2 x 5/2)5/2
= (5)5/2
= 25 (5)1/2
= 25√5

Answer 2

$Given : 4^x - 4^{x - 1} = 24$

$4^{x - 1} (4^1 - 1) = 24$

$4^{x - 1} * 3 = 24$

$4^{x - 1} = \frac{24}{3}$

$4^{x - 1} = 8$

$(2^2)^{x - 1} = 2^3$

$2^{2(x - 1)} = 2^3$

2(x - 1) = 3

2x - 2 = 3

2x = 5

x = 5/2.

Now,

(2x)^x = $(2 * \frac{5}{2})^ \frac{5}{2}$

           = $(5)^ \frac{5}{2}$

           = $5^{2 + \frac{1}{2} }$

           = $5^2 * 5^{ \frac{1}{2} }$

           = $25 * 5^{ \frac{1}{2} }$

           = $25 \sqrt{5}$



Hope this helps!