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# can someone tell me the shortcut for this silly problem?

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can someone tell me the shortcut for this silly problem? [#permalink]  04 Jul 2007, 14:19
can someone tell me the shortcut for this silly problem?

(5^21) x (4^11) = (2 x 10^n) , what is the value of n?

thanks
Intern
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no shortcut, but may be it helps?

5^11*5^10*4^11=2*10^n
(5*4)^11 * 5^10 =
20^10*20*5^10 =
100^10 * 20 = 2 * 10^n | :2
10^10*10^10 * 10 = 10^n
10^21 = 10^n

cya
Mazar
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I would do it a slightyly different way:

(5^21)*(4^11)=2*10^n
(5^21)*(2^22)=2*10^n
(5^21)*(2)(2^21)=2*10^n
2*(5^21)*(2^21)=2*10^n
2*10^21...
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5^21 * 2^22 = 5^21 * 2^21 * 2 = 10^21 * 2

so n = 21
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Re: (5^21) x (4^11) = (2 x 10^n) [#permalink]  04 Jul 2007, 23:45
dzelkas wrote:
can someone tell me the shortcut for this silly problem?

(5^21) x (4^11) = (2 x 10^n) , what is the value of n?

thanks

(5^21)(2^22)=2*(2*5)^n
(5^21)(2^22)=2*2^n*5^n
(5^21)(2^22)=2^n+1*5*n
Equate either term to solve for n

5^21=5^n => n=21
or
2^22=2^n+1 => n=21
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Re: (5^21) x (4^11) = (2 x 10^n) [#permalink]  05 Jul 2007, 20:55
dzelkas wrote:
can someone tell me the shortcut for this silly problem?

(5^21) x (4^11) = (2 x 10^n) , what is the value of n?

thanks

From the expression: 5^21 * (2^2)^11 = 5^21 * 2^22

Now, include this fact: 10 = 5*2

(5*2)^21 * 2 = 10^21 * 2

Therefore, n = ???

Yep, 21.
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Shortcut:

Since you know that there is a 5^21 on the left side. You know that for the equation to be equal, there needs to be exactly 21 5's on the right side. The only way to create 21 5's is to have n=21.
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