
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
December 6th, 2018, 06:54 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 513 Thanks: 80  transcendental equation
How to solve it ? $\displaystyle x=(1)^x$ 
December 6th, 2018, 09:47 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025 
1 = (1)^(1) .... I think!!!

December 6th, 2018, 03:50 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,634 Thanks: 2080 
Does $x$ have to be real?

December 6th, 2018, 05:43 PM  #4 
Senior Member Joined: Aug 2012 Posts: 2,311 Thanks: 706  Reminds me of that great old song, "You got to be real!" That's what I get. $1^{1} = e^{1 \log(1)} = e^{ i \pi} = \frac{1}{e^{i \pi}} = \frac{1}{1} = 1$. I didn't bother to consider the alternate values of $\log i \pi$ but I'll leave that to the reader. Last edited by Maschke; December 6th, 2018 at 05:48 PM. 
December 6th, 2018, 09:39 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,430 Thanks: 1315 
if not $\left( \begin{array}{c} 2.962790.347906 i \\ 4.967310.511894 i \\ 6.97180.619368 i \\ 8.975240.699485 i \\ 10.97790.763401 i \\ 12.980.816587 i \\ 14.98170.862137 i \\ 16.98310.901972 i \\ 18.98430.937368 i \\ 20.98530.969218 i \\ \end{array} \right) $ are a bunch of solutions. Mathematica calls it $\dfrac{i W_{k}(i \pi )}{\pi }$ $W$ is the Lambert W function 
December 7th, 2018, 12:28 PM  #6 
Senior Member Joined: Dec 2015 From: somewhere Posts: 513 Thanks: 80 
Did the Wfunction find $\displaystyle x=1$ ?(without complex x) I dont know how to solve it but i see that solution is $\displaystyle x=1$ What about applying more things if we show at least one equivalence $\displaystyle x=(1)^x \; \leftrightarrow \; x(1)^x =1$ 

Tags 
equation, transcendental 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Nonlinear Transcendental Equation  wuiven64  Real Analysis  4  January 31st, 2018 06:23 PM 
Solving for x in a transcendental equation  Mike Hefner  PreCalculus  2  May 27th, 2016 09:42 AM 
transcendental equation problem  dji321  Trigonometry  4  August 14th, 2015 06:54 PM 
Roots of a transcendental equation  ApplMath  Applied Math  0  November 20th, 2013 06:31 AM 
About some transcendental numbers  Jimmy57  Number Theory  1  April 5th, 2013 06:13 AM 