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Math Help - Solve Exponential Equation with Algebra

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by S8on View Post
    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.
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  3. #3
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    Is it possible with more advanced Algebra then?
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  4. #4
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    Quote Originally Posted by S8on View Post
    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?

    2^x +1 = 4x

    to

    2^x - 1 = x
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  5. #5
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    Quote Originally Posted by S8on View Post
    Is it possible with more advanced Algebra then?
    You'll need to use something called the Lambert W-Function
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  6. #6
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    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.
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  7. #7
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    Quote Originally Posted by S8on View Post
    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.
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  8. #8
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    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.
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  9. #9
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    Quote Originally Posted by S8on View Post
    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.
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