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Now count the 2's. There are 22, so \(4^{11} = 2^{22}\)

RULE: When multiplying numbers with exponents the base numbers (2 is the base of 2^3) can be multiplied if the exponent number is the same. Here we have 5^21 and 2^22. We can pull out a 2 from 2^22 to give us 2^21 * 2 * 5^21. Now we have similar exponent: 21. 5x2 = 10, so we have 2 * 10^21. When you multiply the bases the exponent must be the same, so the exponent remains the same when finished, hence \(5^{21}*2^{21} = 10^{21}\) We pulled out a 2 in order to make the exponent 21 rather than 22 so we have:

2 * 10^21 which makes the value of n = 21.

samlosco wrote:

If 5^21 * 4^11 = 2 * 10^n, what is the value of N?

a) 11 b) 21 c) 22 d) 23 e) 32

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Re: If 5^21*4^11 = 2*10^n, what is the value of n? [#permalink]

Show Tags

04 Dec 2008, 10:48

Answer is B. Here is the approach

5^21 * 4^11 = 2 * 10^n (5^11*5^10) * (2^11*2^10*2) = 2 * 10^n (Rule is = a ^ (m+n) = a ^ m * a * n ) 10^11*10^10* 2 = 2 * 10^n (Multiple the base terms with same powers. a^m * b^ m = ab ^ m) 10^21*2 = 2*10^n

Re: If 5^21*4^11 = 2*10^n, what is the value of n? [#permalink]

Show Tags

13 Feb 2010, 11:13

carriedinterest wrote:

If 5^21 x 4^11 = 2 x 10^n, what is the value of n?

A) 11 B) 21 C) 22 D) 23 E) 32

Clear, concise explanations welcome!

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

Therefore n = 21

B
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carriedinterest, I've seen this a few times - in the middle of a thread, you reprint the question from the first post, asking for 'clear, concise explanations' when there are already one or explanations that have already been provided - perhaps you did not find them clear or concise? In any case, I'm curious why you've done this; you did the same in these threads, for example:

If there is something in the solutions already given that is unclear to you, then it would be more helpful to point that out; surely other test takers share your concerns, and you can all benefit from having that detail of the solution explained. Or, if you are asking if there are alternative solution methods, it would be good to mention that. Otherwise, as has happened in each of these threads, people simply end up typing up the same solutions that were posted above, and I don't know that that benefits anyone much.
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carriedinterest, I've seen this a few times - in the middle of a thread, you reprint the question from the first post, asking for 'clear, concise explanations' when there are already one or explanations that have already been provided - perhaps you did not find them clear or concise? In any case, I'm curious why you've done this; you did the same in these threads, for example:

If there is something in the solutions already given that is unclear to you, then it would be more helpful to point that out; surely other test takers share your concerns, and you can all benefit from having that detail of the solution explained. Or, if you are asking if there are alternative solution methods, it would be good to mention that. Otherwise, as has happened in each of these threads, people simply end up typing up the same solutions that were posted above, and I don't know that that benefits anyone much.

Ian, It was I, who merged the topics as carriedinterest posted several question that were already discussed. Guess I should mentioned this in the thread after doing so. Sorry for confusion.
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Ah, I see - my apologies! It did seem very odd, so I was curious to know why it was happening, but that makes a lot of sense.
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GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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