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# If 5^21 X 4^11 = 2 X 10^n, what is the valve of n?

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Manager
Joined: 05 Aug 2008
Posts: 90
Schools: McCombs Class of 2012
If 5^21 X 4^11 = 2 X 10^n, what is the valve of n? [#permalink]

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17 Dec 2008, 17:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If $$5^2^1 X 4^1^1 = 2 X 10^n$$, what is the valve of n?

(A) 11
(B) 21
(C) 22
(D) 23
(E) 32

E is correct

Can anyone please explain how they solved this problem?

Thank you.
Attachment:

Q2.JPG [ 14.22 KiB | Viewed 926 times ]
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown

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17 Dec 2008, 17:24
B = 21

4^11 = 2^22

4^11 * 5^21 = 2 * 10^21

So, n= 21
SVP
Joined: 07 Nov 2007
Posts: 1764
Location: New York

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17 Dec 2008, 17:24
smarinov wrote:
Can anyone please explain how they solved this problem?

Thank you.
Attachment:
Q2.JPG

$$5^{21} * 4^{11} = 2*10^n$$

$$5^{21}* 2^{22} = 2*10^n$$
$$2*10^{21}= 2*10^{n}$$
n=21
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Intern
Joined: 05 Nov 2007
Posts: 35

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17 Dec 2008, 17:26
smarinov wrote:
Can anyone please explain how they solved this problem?

Thank you.
Attachment:
Q2.JPG

5^21 x 2^22 = 2 x 10^n
5^21 x 2^21 x 2 = 2 x 10^n
(5x2)^21 x 2 = 2 x 10^n
10^21 x 2 = 2 x 10^n
n = 21

B
Manager
Joined: 05 Aug 2008
Posts: 90
Schools: McCombs Class of 2012

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17 Dec 2008, 18:31
You guys are all correct. Thanks for the explanations.
SVP
Joined: 29 Aug 2007
Posts: 2457

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17 Dec 2008, 21:49
smarinov wrote:
Can anyone please explain how they solved this problem?

Thank you.
Attachment:
Q2.JPG

Quick approach: Since 5 to power 21 is in LHS, n has to be 21 because RHS has only unkown, n, a power of 5.

Therefore, it has to be 21.
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Re: Exponents   [#permalink] 17 Dec 2008, 21:49
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# If 5^21 X 4^11 = 2 X 10^n, what is the valve of n?

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