Question

Surds and Indices question!!!

Answer 1

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.

.....Hope it will help.....

Answer 2

i hope this will help you