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Exponent problem (Manhatten ALGEBRA pg 45 #9)

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by DCS80 » Wed Jan 16, 2013 12:53 pm
9) If m and n are positive integers and (2^18)(5^m) = (20^n), what is the value of m?


Open ended, no selections to choose from.

Could you outline each step in words? THANKS!
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by Brent@GMATPrepNow » Wed Jan 16, 2013 1:28 pm
DCS80 wrote:9) If m and n are positive integers and (2^18)(5^m) = (20^n), what is the value of m?
First notice that 4 = 2^2
Also notice that 20^n = (4x5)^n = (4^n)(5^n)

So, we can take (2^18)(5^m) = (20^n) and rewrite it as:
[(2^2)^9][5^m] = [4^n)(5^n)
[4^9][5^m] = (4^n)(5^n)

From this, we can see that m=n (since 5^m must equal 5^n)
And we can see that n = 9, (since 4^9 must equal 4^n)

So, we get n = m = 9

So, [spoiler]m = 9[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by DCS80 » Wed Jan 16, 2013 1:53 pm
edit: nvm, got it

Thanks
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