5^21 x 4^11 = 2 x 10^n. What is n?
Thanks!
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- Anu Nair
Tricky exp qs not so tricky
5^21 * 4^11 = 2 * 10^n
= 5^21 * 2^22
= 5^21 * 2^21 * 2^1
= 10^21 * 2^1
Therefore n=21
= 5^21 * 2^22
= 5^21 * 2^21 * 2^1
= 10^21 * 2^1
Therefore n=21
- RonPurewal
- Students
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- Joined: Tue Aug 14, 2007 8:23 am
There's not much I could do to improve on the solution given here, but here's an item to take away from this problem:
* Consider PRIME FACTORIZATIONS of numbers with exponents. In this case, a 'factor tree' of 4^11 would consist of eleven 4's, which would then break down into twenty-two 2's (giving the correct representation even if you've forgotten the 'common base' concept). Additionally, 10^n would break down into n 5's and n 2's, which would turn the whole right side (including the standalone 2) into n 5's and (n + 1) 2's.
* Consider PRIME FACTORIZATIONS of numbers with exponents. In this case, a 'factor tree' of 4^11 would consist of eleven 4's, which would then break down into twenty-two 2's (giving the correct representation even if you've forgotten the 'common base' concept). Additionally, 10^n would break down into n 5's and n 2's, which would turn the whole right side (including the standalone 2) into n 5's and (n + 1) 2's.
3 posts Page 1 of 1