If 4^x-4^x-1=25,
Then,find the value of x.
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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
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
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