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5^21 x 4^11 = 2 x 10^n

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smritihemdev
 Post subject: 5^21 x 4^11 = 2 x 10^n
 Post Posted: Wed Jul 29, 2009 12:26 pm 
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Course Students


Posts: 1
5^21 x 4^11 = 2 x 10^n

What is n?
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venkat_yj
 Post subject: Re: 5^21 x 4^11 = 2 x 10^n
 Post Posted: Wed Jul 29, 2009 9:34 pm 
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Students


Posts: 16
5^21 x 4^11 = 2 x 10^n

LHS
5^21 x (2^2)^11
5^21 x 2^22

RHS
2 x 10^n
2 x (2x5)^n
2 x (2^n) x (5^n)
2^(n+1) x (5^n)

Now given LHS=RHS
n = 21
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Ben Ku
 Post subject: Re: 5^21 x 4^11 = 2 x 10^n
 Post Posted: Tue Aug 18, 2009 5:26 pm 
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ManhattanGMAT Staff


Posts: 823
When you encounter these problems, you want to use the rules of exponents to equate exponents with the same bases.

We can manipulate the left side:

5^21 * 4^11
= 5^21 * (2^2)^11
= 5^21 * 2^22 because (a^m)^n = a^m*n
= 5^21 * 2^21 * 2^1 because a^m * a^n = a^(m+n)
= (5*2)^21 * 2 because a^m * b^m = (ab)^m
= 2 * 10^21

It's clear that n = 21.

_________________
Ben Ku
Instructor
ManhattanGMAT
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