IF 5^21 x 4^11 = 2 x 10^n what is the value of n?
11
21
22
23
32
The answer is 21 could somebody explain why?
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Exponents, Value of N
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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.
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.
