If X and K are integers and 12^ x * 4 ^ 2x+1 = 2^k*3^2 , what is the value of K ?
5 7 10 12 14
folks please help me out , thanks in advance.
5 7 10 12 14
folks please help me out , thanks in advance.
12^ x * 4 ^ 2x+1 = 2^k*3^2
=>{(3*4)^x}*(4^2x*4)=2^k*3^2
=>3^x*(4^x*4^2x*4)=2^k*3^2
expressing 4 s in powers of 2
=>3^x*2^2x*2^2*2^4x=2^k*3^2
=>3^x*{2^(2x+2+4x)}=2^k*3^2
=>equating powers of 3 on both sides we get x=2
equating powers of 2 on both sides
2^(6x+2)=2^k where x=2
or k=6*2+2=14
14
