gmat prep exponent question

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xcise_science: Master | Next Rank: 500 Posts; Posts: 106; Joined: Tue Oct 09, 2007 12:25 pm; Thanked: 1 times

by xcise_science » Mon Nov 26, 2007 9:08 pm

Someone posted this question before, but I can't find it on the forums, can someone explain it?

5^21*4^11=2(10^n), what is n?

Thanks

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Source: Beat The GMAT — Problem Solving | Mon Nov 26, 2007 9:08 pm

syv11: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Nov 23, 2007 1:36 pm

by syv11 » Mon Nov 26, 2007 9:25 pm

5^21*4^11=2*10^n
5^21*(2^2)^11=2*10^n
5^21*2^(2*11)=2*10^n
5^21*2^22=2*10^n
5^21*2^21=10^n
10^21=10^n
n=21

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xcise_science: Master | Next Rank: 500 Posts; Posts: 106; Joined: Tue Oct 09, 2007 12:25 pm; Thanked: 1 times

by xcise_science » Tue Nov 27, 2007 6:48 am

thanks, but how did you get from here:
5^21*2^22=2*10^n to
5^21*2^21=10^n

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sujaysolanki: Master | Next Rank: 500 Posts; Posts: 214; Joined: Wed Nov 14, 2007 6:30 am; Thanked: 15 times

by sujaysolanki » Tue Nov 27, 2007 6:55 am

2^22 - 2^1 is what being used ...
that gives 2^21 ..then the powers can be combined a ^x * b ^ x = ab ^x
hope that helps

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xcise_science: Master | Next Rank: 500 Posts; Posts: 106; Joined: Tue Oct 09, 2007 12:25 pm; Thanked: 1 times

by xcise_science » Tue Nov 27, 2007 8:38 am

oh, ok, so you subtracted 2 from both sides?
I didn't see that before.

Thanks!

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syv11: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Nov 23, 2007 1:36 pm

by syv11 » Tue Nov 27, 2007 9:14 am

You need to devide it by 2! Not substract!

2^22/2 = 2^(22-1) = 2^21

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