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September 18th, 2018, 02:55 AM   #1
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I need help please

How to find x in this equation:
x^x^x=27
I have tried different methods to solve that with no success.
I tried to take logarithm from both sides but it ended up with mess.
I put x^x=y and tried to solve x^y=3^3 but nothing further after that.
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September 18th, 2018, 04:16 AM   #2
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Apply Newton's method to the function $f(x) = x^{x^x} - 27$.
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September 18th, 2018, 05:41 AM   #3
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Where did you get this problem from?
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September 18th, 2018, 06:55 AM   #4
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Quote:
Originally Posted by skipjack View Post
Where did you get this problem from?
From my daughter.
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September 18th, 2018, 08:29 AM   #5
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Does your daughter know where it came from or did she make it up?
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September 18th, 2018, 08:34 AM   #6
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Quote:
Originally Posted by skipjack View Post
Does your daughter know where it came from or did she make it up?
She is doing her final year in high school and she got it from her friend.
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September 18th, 2018, 09:10 AM   #7
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Could the question have been x^x = 27 originally, but got changed in the course of being passed on from person to person?
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September 18th, 2018, 10:06 AM   #8
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Quote:
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Could the question have been x^x = 27 originally, but got changed in the course of being passed on from person to person?
No, I asked the same thing. The question is correct.
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September 18th, 2018, 06:50 PM   #9
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In that case, there doesn't seem to be a closed expression that gives x explicitly.
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September 26th, 2018, 05:49 PM   #10
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This isn't an exact answer, but my graphing calculator says x is about 2.1046.
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