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# PS Exponent help plz

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Intern
Joined: 19 Mar 2008
Posts: 14

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29 Mar 2008, 20:45
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is there an easy way to solve this that doesn't take forever?

5^21 x 4^11 = 2 x 10^n
solve for n

Director
Joined: 10 Sep 2007
Posts: 938
Re: PS Exponent help plz [#permalink]

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29 Mar 2008, 20:56
4^11 = 2^22
So 5^21 x 4^11 = 5^21*2^22 = 2*10^21
2*10^21 = 2*10^n
=> n=21

I think took 30 second for me to type this answer and may be not more than 5 seconds to solve it. I am not sure how quickly you want the answer.
Manager
Joined: 27 Mar 2008
Posts: 53
Re: PS Exponent help plz [#permalink]

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29 Mar 2008, 20:59
This is a question that tests your manipulation abilities for exponents

5^21 x 4^11 = 2 x 10^n
[(5)^21][(2)(2)]^11 = (2)[(2)(5)]^n
[(5)^21][2^22] = [2^(1+n)][5^n]

Here you can see that if we only look at the exponents with base 5, we get n=21. If we only look at the base 2 exponents, we get 22=n+1 which also gives n = 21
Re: PS Exponent help plz   [#permalink] 29 Mar 2008, 20:59
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