Quick questions with Exponents

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KMart87: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Tue May 26, 2009 4:26 pm

by KMart87 » Thu Jun 11, 2009 9:54 am

Had trouble with these three questions:

5^21 * 4^11= 2x * 10n
Ans: 21?

(Radical2 + RAdical5)^2
Ans: ~13?

2^x -2^x-2= 3(2^13)
Ans: 15?

I think I'm missing a key concept here. Can anyone help me out?

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Source: Beat The GMAT — Problem Solving | Thu Jun 11, 2009 9:54 am

gmahendru: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Mar 30, 2008 2:50 am; Thanked: 2 times

by gmahendru » Thu Jun 11, 2009 6:48 pm

1) 5^21 * 2^22 = 2^(x+n) * 5^n

so 5^21 = 5^n
n = 21

2) (rad2 + rad5)^2
= 2 + 5 + 2(rad10)
~ 7 +6
~ 13

3) 2^x -2^(x-2)= 3(2^13)

2^(x-2) [2^2 - 1] = 3*2^13
(x-2) = 13
x= 15

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