We were given the problem 2^x+1=4x from the book and it was asked of us to solve using a table and graphing. I am interested in anyways to solve without either and just using Logs, their properties and algebra. Is it possible?
(I have simplified it down to 2^x-1=x and the answer is easily found with guess and check to be 2 and 1, so I am guessing you have to somehow find x^2-3x+2)
Thanks in advance
You'll need to use something called the Lambert W-Function
I meant 2^(x-1)=x from 2^(x+1)=4, srry for the confusion. Also, I looked it up elsewhere and Lambert function kept coming up, but it didn't really help much on Wikipedia and I'm too dumb to understand the explanation of it, but I hope to understand it with your guys help or with examples or the process of solving this equation.
The standard reference on the Lambert W-function is this: http://www.cs.uwaterloo.ca/research/tr/1993/03/W.pdf. Read it.
But as I said earlier, it is above and beyond what you're meant to do in the given question.
And as you said yourself:
a clear indcator that you do not have the necessary background at this stage for understanding this function. I do not have the time or the inclination to provide you with personal tuition on this function and the background required for understanding it. Someone else might.Also, I looked it up elsewhere and Lambert function kept coming up, but it didn't really help much on Wikipedia and I'm too dumb to understand the explanation of it,