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April 16th, 2014, 04:17 AM   #1
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solve

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x^x^x^16 =16
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April 16th, 2014, 09:13 AM   #2
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Quote:
Originally Posted by mared View Post
solve
x^x^x^16 =16
k = x^x^x

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

...carry on....
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April 16th, 2014, 09:21 AM   #3
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x^x^x^16 means x^(x^(x^16)), not (x^x^x)^16. Carry on...
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April 16th, 2014, 07:57 PM   #4
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Quote:
Originally Posted by skipjack View Post
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!).
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April 16th, 2014, 10:46 PM   #5
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$\displaystyle x=1.1892071150027$

Last edited by mhacker064; April 16th, 2014 at 10:48 PM.
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April 17th, 2014, 12:01 AM   #6
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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 )
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April 17th, 2014, 02:19 AM   #7
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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.
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April 17th, 2014, 03:34 AM   #8
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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.
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April 17th, 2014, 06:02 AM   #9
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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.
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April 17th, 2014, 06:25 AM   #10
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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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