If x and k are integers and (12^x) (4^2x+1) = (2^k) (3^2), what is the value of k?
a. 5
b. 7
c. 10
d. 12
e. 14
a. 5
b. 7
c. 10
d. 12
e. 14
here it goes
(12^x) (4^2x+1) = (2^k) (3^2)
[(2*2*3)^x] * [2^2(2x+1)]=(2^k) (3^2)
-->(2^2x) * (3^x)*(2^4x+2)=(2^k) (3^2)
--> equatin for x and k
first powers of 3
we get
3^x=3^2
where x=2
now for powers of 2
we get
2x+4x+2=k
6x+2=k
but we know x=2
6(2)+2=14
k=14
Vishu
