Is there a simple way to solve this problem from GMAT Prep?
5^21 x 4^11=2 x 10^n What is n?
a) 11
b)21
c)22
d) 23
e) 32
The official answer is 21.
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Exponent Question--GMAT Prep
This topic has expert replies
You can factorize the equation to its prime factors.
5^21 x 4^11=2 x 10^n
5^21 x 2^22 = 2 x 2^n x 5^n
5^21 x 2^22 = 2^(n+1) x 5^n
We can equate powers of either prime factor 2 or 5.
i.e. 5^21 = 5^n, gives n = 21
Or, 2^22 = 2^(n+1), gives n = 21
5^21 x 4^11=2 x 10^n
5^21 x 2^22 = 2 x 2^n x 5^n
5^21 x 2^22 = 2^(n+1) x 5^n
We can equate powers of either prime factor 2 or 5.
i.e. 5^21 = 5^n, gives n = 21
Or, 2^22 = 2^(n+1), gives n = 21
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marvelxx35
- Newbie | Next Rank: 10 Posts
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when given 5^21 * 4^11 = 2 * 10^n,
simplify 4^11 to 2^22 to get, 5^21 * 2^22 = 2 * 10^n.
then, simplify again to get, 10^21 * 2 = 2 * 10^n.
you can clearly see that n = 21.
simplify 4^11 to 2^22 to get, 5^21 * 2^22 = 2 * 10^n.
then, simplify again to get, 10^21 * 2 = 2 * 10^n.
you can clearly see that n = 21.
