Thread: Solve Exponential Equation with Algebra

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

Originally Posted by S8on

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?

Thanks in advance

No it's not possible using basic algebra.

Is it possible with more advanced Algebra then?

Originally Posted by S8on

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

How did you simplify?



to

Originally Posted by S8on

Is it possible with more advanced Algebra then?

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.

Originally Posted by S8on

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 problem was designed to be done in a particular way. Concentrate on understanding that. The Lambert W-function is almost certainly beyond your present ability to understand.

My effort is consistent. I will try and find a way to solve this and understand. Please just help a little in explanation? If it is beyond my ability to comprehend, I will make it within my ability to understand.

Originally Posted by S8on

My effort is consistent. I will try and find a way to solve this and understand. Please just help a little in explanation? If it is beyond my ability to comprehend, I will make it within my ability to understand.

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:

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,

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.