Question

4^x-4^x-1 = 24, then find the value of (2x)^x
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Answer 1

Answer:

Step-by-step explanation:

 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

Answer:

4^x-4^x-1 = 24

so, (4^x * 1)-(4^x * 1/4) = 24

so, 4^x ( 1 - 1/4)= 24

so, 4^x ( 3/4)= 24

so, 4^x = 24*4/3

so, 4^x = 32

so, 2^2x = 2^5

so, 2x = 5 [since the bases are equal therefore the powers are also equal]

so, x = 5/2

(2x)^x

=(2*5/2)^5/2

=(5)^5/2

=25 underroot 5   (Ans)