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Exponents, Value of N

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by DanaJ » Sat May 02, 2009 9:07 am
This question has been answered many times before. But here goes:

10^n = (2*5)^n = (2^n)*(5^n). This means that:

2 * 10^n = 2*(2^n)*(5^n) = [2^(n+1)]*(5^n).

Now, look at the left side: 4^11 = (2^2)^11 = 2^22.

So you have:

(5^21)*(2^22) = [2^(n+1)]*(5^n).

This is why n = 21.
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