BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

what is the value of K

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 129
Joined: Mon Dec 15, 2008 11:43 pm
Location: Hyderabad
Thanked: 2 times

what is the value of K

by naaga » Thu Mar 05, 2009 4:01 am
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.
Top
Source: — Problem Solving |
Legendary Member
Posts: 1035
Joined: Wed Aug 27, 2008 10:56 pm
Thanked: 104 times
Followed by:1 members

by scoobydooby » Thu Mar 05, 2009 5:10 am
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
Top
Post new topic Post Reply
• Page 1 of 1