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31 Jul 2008, 13:13
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Hi All, would someone please help explain this question? It's from GMAP Prep 1. Many thanks.
5^21 * 4^11 = 2 * 10^N
N=?
5^21 * 4^11 = 2 * 10^N
N=?
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31 Jul 2008, 13:15
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I like this problem a lot. Hopefully I can help.
If you change the 4^11 into (2^2)^11, then it becomes 2^22.
Now, if you look at the left side, you have 21 5's being multiplied by 22 2's. If you match up a 5 and 2, you'll get 21 pairs of 5*2 with one 2 left over. Turn those 21 pairs of a 5 and 2 into 10 and you're left with 21 10's multiplied together and then multiplied by 2.
That equals 2* (10^21) so N=21.
Algebraically, (ab)^c = a^c * b^c as a rule of exponents. After changing 4^11 into 2^22 you can apply this rule backwards as 5^21 * 2^21 * 2 = (5*2)^21 * 2 = 2* (10^21), N = 21
If you change the 4^11 into (2^2)^11, then it becomes 2^22.
Now, if you look at the left side, you have 21 5's being multiplied by 22 2's. If you match up a 5 and 2, you'll get 21 pairs of 5*2 with one 2 left over. Turn those 21 pairs of a 5 and 2 into 10 and you're left with 21 10's multiplied together and then multiplied by 2.
That equals 2* (10^21) so N=21.
Algebraically, (ab)^c = a^c * b^c as a rule of exponents. After changing 4^11 into 2^22 you can apply this rule backwards as 5^21 * 2^21 * 2 = (5*2)^21 * 2 = 2* (10^21), N = 21
31 Jul 2008, 13:19
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imadummy
5^21 * 4^11 = 2 * 10^N
-->
5^21 * (2*2)^11 = 2 * 10^N
-->
5^21 * (2)^22 = 2 * 10^N
5^21 * (2)^21 = 10^N
(5*2)^21 = 10^N
(10)^21 = 10^N
-->N=21
