Question

If 4^x - 4^x-1=24,then(2x)^x equals

Answer 1

4^x - 4^x-1 =24
4^x - 4^x/4 = 24
multiply each term with 4

4 *4^x - 4^x = 24*4
take 4^x common
4^x (4-1) = 24*4
4^x * 3= 24*4
4^x = 24*4/3
4^x =32

2^2x =2^5
therefore
2x = 5---(1)
x= 5/2---(2)

required (2x)^x = (5)^5/2 from (1) and (2)

= (5^5)1/2
= √(5*5)*(5*5)*5
=25√5