Question 1034772: log(x)^log(x) = 506
Please show how one would solve for x? Found 2 solutions by Theo, Edwin McCravy:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! i can solve this graphically but i haven't figured out how to solve it algebraically.
graphically, i solve it as follows:
set y1 = log(x)^log(x)
set y2 = 506
graph both equations using graphing software or graphing calculator such as ti-84 plus.
using the ti-84 plus, you will get the intersection of both graphs is when x = 19119.3959
it's a little tricky to get it, but it can be done.
if you replace x in the original equation, you will get:
log(19119.3959)^(log(19119.3959) = 506.
the solution to this problem is x = 19119.3959.
algebraically is another story.
i haven't figured out how to do that yet.
you could probably also solve it by iteration, but that's the hard way, since it takes many iterations to narrow it down sufficiently.
here's a picture of my graphical solution with the results rounded to 3 decimal places.
x is approximately 19119.3959 if the log has base 10
x is approximately 72.34701295 if the log has base e (natural log)
There are no algebraic techniques to handle this.
The only way is by technology, perhaps a TI-84.
Edwin
