Monu631
As per the question, 4^x - 4^x-1 = 24 We can rewrite it as, 4^x - 4^x *4^(-1) =24 4^x(1-4^-1) = 24 4^x (1-1/4) = 24 4^x *3/4 = 24 4^x * 1/4 = 8 4^x-1 = 8 2^ 2(x-1) = 2^3 By equating the powers, as the base is equal so power should also be equal. 2(x-1) = 3 x-1 = 3/2 x = 3/2 +1 =5/2. Now, we have to find (2x)^x So, (2*5/2)^5/2 = (5)^5/2 = 25√5 . Option C will be the answer.
Answers & Comments
4^x - 4^x-1 = 24
We can rewrite it as,
4^x - 4^x *4^(-1) =24
4^x(1-4^-1) = 24
4^x (1-1/4) = 24
4^x *3/4 = 24
4^x * 1/4 = 8
4^x-1 = 8
2^ 2(x-1) = 2^3
By equating the powers, as the base is equal so power should also be equal.
2(x-1) = 3
x-1 = 3/2
x = 3/2 +1 =5/2.
Now, we have to find (2x)^x
So, (2*5/2)^5/2 = (5)^5/2 = 25√5 .
Option C will be the answer.
.....Hope it will help.....