My Math Forum I need help please

 Algebra Pre-Algebra and Basic Algebra Math Forum

 September 18th, 2018, 02:55 AM #1 Newbie   Joined: Mar 2017 From: Norway Posts: 12 Thanks: 0 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.
 September 18th, 2018, 04:16 AM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 522 Thanks: 297 Math Focus: Dynamical systems, analytic function theory, numerics Apply Newton's method to the function $f(x) = x^{x^x} - 27$.
 September 18th, 2018, 05:41 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,003 Thanks: 1862 Where did you get this problem from?
September 18th, 2018, 06:55 AM   #4
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Joined: Mar 2017
From: Norway

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Quote:
 Originally Posted by skipjack Where did you get this problem from?
From my daughter.

 September 18th, 2018, 08:29 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,003 Thanks: 1862 Does your daughter know where it came from or did she make it up?
September 18th, 2018, 08:34 AM   #6
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Joined: Mar 2017
From: Norway

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Quote:
 Originally Posted by skipjack 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.

 September 18th, 2018, 09:10 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,003 Thanks: 1862 Could the question have been x^x = 27 originally, but got changed in the course of being passed on from person to person?
September 18th, 2018, 10:06 AM   #8
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From: Norway

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Quote:
 Originally Posted by skipjack 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.

 September 18th, 2018, 06:50 PM #9 Global Moderator   Joined: Dec 2006 Posts: 20,003 Thanks: 1862 In that case, there doesn't seem to be a closed expression that gives x explicitly. Thanks from Farzin
 September 26th, 2018, 05:49 PM #10 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 623 Thanks: 85 This isn't an exact answer, but my graphing calculator says x is about 2.1046.

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