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

Redeem

Integer

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 190
Joined: Thu Jan 14, 2010 8:29 pm
Thanked: 2 times

Integer

by phoenix9801 » Thu Jun 17, 2010 6:28 am
I need some clarification of the 2 problems please. If you can explain step-by-step instruction I would greatly appreciate it. Be Simple...


If x and k are integers and (12^x)(4^2x+1) = (2^k) (3^2), what is the value of K.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

by kvcpk » Thu Jun 17, 2010 6:38 am
rewrite it as

2^2x * 3^x * 4^2x+1 = 2^k * 3^2
2^6x+2* 3^x = 2^k * 3^2
so x = 2

6x+2 = k
therefore k =14
Last edited by kvcpk on Thu Jun 17, 2010 7:43 am, edited 1 time in total.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 294
Joined: Wed May 05, 2010 4:01 am
Location: india
Thanked: 57 times

by amising6 » Thu Jun 17, 2010 7:29 am
If x and k are integers and (12^x)(4^2x+1) = (2^k) (3^2), what is the value of K. ( i am assuming 4^(2x+1) i.e 4 to the power of (2x+1)

12^x=(2*2*3)^x=2^2x *3^x
4^2x+1=(2^2)^2X*2^2=2^(4x+2)
so we have now
(12^x)(4^2x+1) = (2^k) (3^2)
(2^2x *3^x)(2^(4x+2))=(2^k) (3^2),
2^(2x+4x+2).3^x=(2^k) (3^2)
L.H.S=R.H.S
so we can say 2^(2x+4x+2).= 2^k ----equation 1
3^x= (3^2) --- equation 2
since both base is 3 we can conclude x=2
now replacing value of x in equation 1
2^(2x+4x+2).= 2^k
since base is 2
we can equate 2x+4x+2=k
6x+2=k
6*2+2=k now replacing value of x
hence k=14
Ideation without execution is delusion
Top
Post new topic Post Reply
• Page 1 of 1