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karovd
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 02:00
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If X=10^100,

X^X= 10^K. What is the value of K?



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maaverick
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 03:13
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x = 10^100 - (1)

Also, x^x = 10^k - (2)

Taking logarithm base 10 on both sides of (2)

x (log x) = k (log 10)

Log 10 to base 10 = 1

=> k = x log x

=> k = 10^100 (log (10^100))

=> k = 100 (10^100) = (10^2) * (10^100)

=> k = 10^102
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karovd
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 03:37
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Thanks, using log is a good method to solve exponential problems, esp exponential on exponential ones. Think I've returned everything to the school teacher already! :lol:
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twixt
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 03:47
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Log base 10 is a great idea to solve this one and maaverick reasoning is clear. I do not see any flaw anyway without using it and just looking at X structure I obtain K = 2.10^100

It is hard to believe that (10^100)^(10^100) = 10^(10^102)
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 07:26
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I got 10^102 as well.

x = 10^100

x^x = 10^k

x^x = (10^100)^(10^100) = 10^(100*10^100)

=> k = 100(10^100) = 10^102

It never occurred for me to use log! Thanks maaverick, its always good to know different ways to solve a problem. :-D
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revital
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 09:26
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can you explain how did you get it in more details , I dont get it :-(
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rthothad
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 09:38
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One more 10^102.

x = 10^100

x^x = 10^k => x = 10^k/x

So, 10^k/x = 10^100
=> k/x = 100

k = 100x = 100 * 10^100 = 10^102
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Paul
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If X=10^100, X^X= 10^K. What is the value of K 24 Nov 2004, 10:37
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Yet a slight variation, done in less than 1 min:
Try to get everything to base 10 since 10^k is what you are looking for
x^x = 10^(100 * 10^100)
= 10^(10^2 * 10^100)
= 10^(10^102) = 10^k
k = 10^102



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