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x=10^100, x^x=10^k, k=

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x=10^100, x^x=10^k, k= [#permalink] New post 09 Aug 2006, 00:39
x=10^100, x^x=10^k, k=?
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 [#permalink] New post 09 Aug 2006, 04:39
x^x=10^k
=> (10^100)^(10^100) = 10^k
=> 10^(10^102) = 10^k

k= 10^102
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10^102 [#permalink] New post 09 Aug 2006, 06:02
x^x = 10^k
so xlogx = k
so 10^100 log (10^100)
so 10^100 *100 log 10
so 10^102
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 [#permalink] New post 09 Aug 2006, 07:58
k=102

100*10^100=10^k
10^102=10^k
thus k=102
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 [#permalink] New post 09 Aug 2006, 09:29
k = 10^102

x^x = 10^k
x= 10^100

x^x =((10^100)^(10^100))
= (10^(100x(10^100)))
= (10^(10^2x10^100))
= (10^(10^102))

k = 10^102
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 [#permalink] New post 09 Aug 2006, 09:42
10^100 = 10000.......100 zeros.........

x^x = (10^100)^ (1000........100 zeros)
= 10^(1000....102 zeros)
so k = 102
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 [#permalink] New post 09 Aug 2006, 09:46
ps_dahiya wrote:
10^100 = 10000.......100 zeros.........

x^x = (10^100)^ (1000........100 zeros)
= 10^(1000....102 zeros)
so k = 102


Isn't k = (1000....102 zeros) = 10^102?
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 [#permalink] New post 09 Aug 2006, 09:52
haas_mba07 wrote:
ps_dahiya wrote:
10^100 = 10000.......100 zeros.........

x^x = (10^100)^ (1000........100 zeros)
= 10^(1000....102 zeros)
so k = 102


Isn't k = (1000....102 zeros) = 10^102?

:oops Indeed it is 10^102
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 [#permalink] New post 09 Aug 2006, 12:48
x=10^100 or 10^10^2

x^x=10^(10^2)*10^100=10^102=10^K
k=10^102
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 [#permalink] New post 09 Aug 2006, 16:48
Can somone please send me a page where I can learn this technique?
Really, this is the last thing I need to learn
I have tried every single GMAT prep course and nothing has helped:(
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 [#permalink] New post 11 Aug 2006, 02:25
x=10^100

x^x = (10^100)^10^100
= [10^(10^2*10^100)]
= 10^(10^102)
10^k = 10^(10^102)
K = 10^102
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 [#permalink] New post 11 Aug 2006, 09:54
I totally don't get this. Can someone explian this problem SLOWLY?

Thanks!!!!
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 [#permalink] New post 11 Aug 2006, 10:12
Please explain what I'm getting wrong here:

sure 100 * 10^100 would equal 10^102

But this is 100 ^ 10^100

How is this still 10^102?


Am I missing something really simple? Thanks!!!
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 [#permalink] New post 11 Aug 2006, 10:26
nothanks wrote:
Please explain what I'm getting wrong here:

sure 100 * 10^100 would equal 10^102

But this is 100 ^ 10^100

How is this still 10^102?


Am I missing something really simple? Thanks!!!

x=10^100
we need to find x^x

x = 10^100 = 100000............100 zeros.......... let this be equal to y
100y = 100000.............102 zeros................ = 10^102

Now x^x = x^y
(10^100)^y
= 10^100y
= 10^(10^102)
This is equal to 10^q
so 10^(10^102) = 10^q
hence q = 10^102

Hope this helps
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 [#permalink] New post 11 Aug 2006, 11:22
I just figured it out. In case anyone else is having a tough time (seems like it's only me!) here is how I got it.

get rid of the first 10^ as it is not important for finding the answer.

so it's

100^10^100

We can break that down to

1^100 * 1^10^100

Further...

1^10^2 * 1^10^100

Even Further...

1^10^102

And finally

10^102

I feel kind of foolish for not making the connection sooner. Oh well...
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 [#permalink] New post 12 Aug 2006, 07:32
This problem is easier if you know logs:

x = 10^100
therefore log x = 100 (1)

x^x = 10^k
therefore xlogx = k
substitute from (1) above:

x(100) = k

therefore k = 100.10^100 = 10^2.10^100 = 10^(100+2) = 10^102


haas_mba07 wrote:
ps_dahiya wrote:
10^100 = 10000.......100 zeros.........

x^x = (10^100)^ (1000........100 zeros)
= 10^(1000....102 zeros)
so k = 102


Isn't k = (1000....102 zeros) = 10^102?
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 [#permalink] New post 12 Aug 2006, 18:12
gx^x=(10^100)^(10^100)
= 10^(100^(10^100)

X^x=10^k
Take logs.
Xlogx=klog10=k
10^100(log10^100)=k
10^100(100)=k
10^100*10^2=k
10^102=k
  [#permalink] 12 Aug 2006, 18:12
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