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

M4maths Previous Puzzles

06 Mar 2013 equation

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

OPtion

1) 8*sqrt5
2) 25*sqrt5
3) sqrt5
4) 125
5) 3
6) 3*sqrt5
7) 125*sqrt5
8) 5*sqrt5
9) 25
10) None of these

Solution

solve equation
x = 5/2
then(2x)^x = 25*sqrt5

Correct Option: 2 Best Solution (6)

Dr.Dipin Singh   12 years AGO

4^x-(4^(x-1))=24
4^(x-1)[4-1]=24
4^(x-1)=24/3=8
2^(2x-2)=2^3
2x-2=3
2x=5
x=5/2
then (2x)^x = 5^(2.5)= (5^2)* sqrt 5=25 sqrt5

Like? Yes (19) | No (12)  

M sai pratap Reddy   12 years AGO

4^x- 4^(x-1)=24
multiply 4^x with 4*4^-1
4*4^-1 *4^x - 4^(x-1)=24
4*4^(x-1) - 4^(x-1)=24
take 4^(x-1) as common
4^(x-1)[4-1]=24
4^(x-1)=8
we can write 4 as 2^2
2^(2x-2)=2^3
2x-2=3
2x=5 => x=5/2
(2x)^x => (2*5/2)^5/2
(sqrt5)^5=>> 25*sqrt5

Like? Yes (9) | No (11)  

Mukesh Kr Singh   12 years AGO

let 4^x=a
then
a-a/4=24
a=32

therefore
4^x=32
i.e.,2^2x=2^5
i.e,2x=5
so,(2x)^x=(5)^(5/2)=25*sqrt5

Like? Yes (11) | No (14)  

ArunKumar   12 years AGO

4^x-(4^(x-1))=24
4^x(1-4^(-1))=24
4^x(1-1/4))=24
4^x=24 * 3/4
2^(2x)=2^5
x = 5/2
Now (2x)^x = (2*5/2)^(5/2)
= 5 ^ (5/2)
= 25* sqrt(5)

Like? Yes (8) | No (11)  

sumit jindal   12 years AGO

2^2x-(2^(2x-1))=24
(2^(2x-2))(4-1)=24
(2^2x)/4=8
2^2x=32
2^2x=2^5
x=5/2
so (2x)^x=5^(5/2)
=25*sqrt5= 2) ans

Like? Yes (9) | No (13)  

Balakrishnan M   12 years AGO

(4^x)-(4^(x-1))=24
(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)= 24*(4/3)
(4^x)= 32
(4^x)=(4^2)*2 = (4^2)*(4^(1/2))
(4^x)= 4^(2+(1/2))
(4^x)= 4^(5/2)
x = 5/2
then (2x)^x = [2*(5/2)]^(5/2)
= 5^(5/2)=5^(2+(1/2))
=(5^2)*sqrt5
= 25*sqrt5

Like? Yes (6) | No (13)