All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
Powers of powers (Posted on 2004-05-11) Difficulty: 3 of 5
Solve for x, if:
x    = 3
An algebraic solution is sought!

See The Solution Submitted by Federico Kereki    
Rating: 4.1000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Power Tower | Comment 5 of 11 |

Substitute x^(x^(x^3)) for the three in the exponent to get:
x^(x^(x^(x^(x^(x^3))))) = 3
x^(x^(x^(x^(x^(x^(x^(x^(x^3)))))))) = 3

And repeat ad infinitum to get an infinite power tower:
x^(x^(x^(x^(x^(x^(x^(x^(x^(.........))))))))) = 3

Now the exponent of the bottom x is identical to the entire expression, so 3 can be substituted to yield x^3 = 3

The value x = cbrt(3) is the solution to all of the equations.

  Posted by Brian Smith on 2004-05-11 15:29:34
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information