Problem factgoring exponents

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centermass1976: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Sep 30, 2008 3:56 pm

by centermass1976 » Sat Oct 04, 2008 4:22 pm

Hi everybody, great site!

I am having a problem with this algebra problem. This has been addressed on other posts, but I don't understand the second line. Problem is:
10. 2^x - 2^(x-2) = 3*2^13
=> 2^(x-2)[2^2 - 1] = 3*2^13
=> 2^(x-2) *3 = 3*2^13
comparing
x-2=13
=> x=15(ANS)

------I don't understand how to get from the original problem to the second line of: 2^(x-2)(s^2-1)=... Thanks for your help--Clint

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Source: Beat The GMAT — Problem Solving | Sat Oct 04, 2008 4:22 pm

Sachindh: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Wed Sep 17, 2008 8:17 pm; Location: India; Thanked: 4 times

Re: Problem factgoring exponents

by Sachindh » Sat Oct 04, 2008 6:20 pm

centermass1976 wrote:Hi everybody, great site!

I am having a problem with this algebra problem. This has been addressed on other posts, but I don't understand the second line. Problem is:
10. 2^x - 2^(x-2) = 3*2^13
=> 2^(x-2)[2^2 - 1] = 3*2^13
=> 2^(x-2) *3 = 3*2^13
comparing
x-2=13
=> x=15(ANS)

------I don't understand how to get from the original problem to the second line of: 2^(x-2)(s^2-1)=... Thanks for your help--Clint

2^x-2^(x-2)=3*2^13
Consider LHS only. We can write
2^(x-2)*2^2 - 2^(x-2) where as 2^(x-2)*2^2 = 2^(x-2+2)=> 2^(x)
therefore we can write
2^(x-2)[2^2-1]

I hope this explains you.

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vishubn: Legendary Member; Posts: 574; Joined: Sun Jun 01, 2008 8:48 am; Location: Bangalore; Thanked: 28 times

by vishubn » Sat Oct 04, 2008 6:33 pm

I am having a problem with this algebra problem. This has been addressed on other posts, but I don't understand the second line. Problem is:
10. 2^x - 2^(x-2) = 3*2^13

alternate approach ....

2^x - 2^(x-2) = 3*2^13
-->2^x-(2^x/2^2)=3*2^13
-->(2^2*2^x-2^x)=3*2^15
-->2^x(2^2-1)=3*2^15
2^x*3=3*2^15

x=15

HTH
vishu

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Oct 04, 2008 7:17 pm

One more approach

2^x - 2^ (x-2)
= 2 ^ x - (2^x * 2 ^ -2)
Take 2^x common factor out

= 2^x(1-2^-2)
= 2^x (1-1/4) = 3 * 2 ^ 13
= 2 ^ x(3/4) = 3 * 2 ^ 13
= 2 ^ x * 3 = 3 * 2 ^ 13 * 2 ^ 2
= 2 ^ x * 3 = 3 * 2 ^ 15

x = 15

I guess there are different ways to skin a cat and u choose what works best for u!!!

Good luck!

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Oct 04, 2008 7:21 pm

Explainign a little further:

2^x - 2^ (x-2)
= 2 ^ x - (2^x * 2 ^ -2) (using exponent rule a ^ m+n = a ^m * a ^ n where a =2 m =x n= -2)

Take 2^x common factor out

= 2^x(1 - 2^-2) (using exponent rule a ^ -m = 1 / a ^m)
= 2^x * (1 - 1 /4) = 3 * 2 ^ 13
= 2 ^ x * (3/4) = 3 * 2 ^ 13
= 2 ^ x * 3 = 3 * 2 ^ 13 * 2 ^ 2 (since 4 = 2 ^ 2)= 2 ^ x * 3 = 3 * 2 ^ 15

x = 15

Hope this helps!

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