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 April 16th, 2014, 04:17 AM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 solve solve x^x^x^16 =16
April 16th, 2014, 09:13 AM   #2
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Quote:
 Originally Posted by mared solve x^x^x^16 =16
k = x^x^x

k^16 = 16
k = 16^(1/16)

...carry on....

 April 16th, 2014, 09:21 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,937 Thanks: 2210 x^x^x^16 means x^(x^(x^16)), not (x^x^x)^16. Carry on...
April 16th, 2014, 07:57 PM   #4
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Quote:
 Originally Posted by skipjack x^x^x^16 means x^(x^(x^16)), not (x^x^x)^16. Carry on...
I had written short numeric program;
x^x^x^16 = 16 ; x = ~1.14208

Just went back and changed to what you show:
x^(x^(x^16)) = 16 ; x = ~1.18921

I'm surprised that the change from x^x^x^16 to x^(x^(x^16))
is not automatic (not in UBasic anyway).
So shouldn't the OP have included the brackets then?

Thanks for stepping in Skip; can you clarify (I'm also a learner!).

 April 16th, 2014, 10:46 PM #5 Newbie   Joined: Apr 2014 From: india Posts: 3 Thanks: 0 $\displaystyle x=1.1892071150027$ Last edited by mhacker064; April 16th, 2014 at 10:48 PM.
 April 17th, 2014, 12:01 AM #6 Senior Member   Joined: Apr 2014 From: UK Posts: 955 Thanks: 342 I took the original to mean ((x^x)^x)^16 = 16 giving x =~1.14208 I believe this is the correct answer because you work from left to right (and that's what the web tells me too )
 April 17th, 2014, 02:19 AM #7 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra I agree with Skipjack: the expression should be interpreted as $\displaystyle x^{x^{x^{16}}}$. If we wanted it to mean the other one, we could have written $\displaystyle x^{16x^2}$ instead.
 April 17th, 2014, 03:34 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,937 Thanks: 2210 The usual interpretation regarding order of operations is what I gave, as the alternative interpretation allows easy simplification. For this problem, it turns out that one can add extra occurrences of "x^" without affecting the final answer. Last edited by skipjack; April 17th, 2014 at 03:38 AM.
 April 17th, 2014, 06:02 AM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Interesting stuff... Using k=x^x^x then k = 16^(1/16) = 1.1892071... Now we have x^x^x = 1.1892071, so x = 1.1420819... In UBasic: x = 1.1420819 PRINT x^x^x^16 Output: ~16 Looks like that in programming languages, the "brackets" need to be included.
 April 17th, 2014, 06:25 AM #10 Senior Member   Joined: Apr 2014 From: UK Posts: 955 Thanks: 342 This is why I like brackets.... Wolfram agrees with it being x^(x^(x^16)) This page has an example with the right answer, but the wrong explanation! Order of Operations - GMAT Math Study Guide problem 2 at the bottom...

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