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Homework Help: Exponential Equation! -Stuck -

  1. Feb 7, 2010 #1
    Exponential Equation! -Stuck!!-

    1. 32y+3 = 3y+5


    3. The attempt at a solution

    2y + 3 = y+5
    2y = y+2


    I really don't think I am doing this right, I am trying to find the value of Y. the answer is 2 but I don't know how to come up with the answer.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 7, 2010 #2
    Re: Exponential Equation! -Stuck!!-

    The progress looks great to me! The next step is to get all of the y-terms on one side of the equation. :smile:
     
  4. Feb 7, 2010 #3
    Re: Exponential Equation! -Stuck!!-

    So then would it be 2y + y = 2 or 2y2 = 2?
     
  5. Feb 7, 2010 #4
    Re: Exponential Equation! -Stuck!!-

    These two equations are not equivalent. Let us ignore the 2y2 = 2 for now. Your previous step left the equation at 2y = y + 2. Remember that if you add or subtract a value from one side of the equation, you have to do the same thing to the other side. Therefore, in the first equation in the quote you have 2y + y = 2, but this is not the same as 2y = y + 2 because you added one y to the left side but subtracted the y from the right side. If you add y to the left, then you must add y to the right, getting 2y + y = y + y + 2.

    Instead of this, can you think of what to do to both sides of the equation that would result in having no y on the right side of the equation?
     
  6. Feb 7, 2010 #5
    Re: Exponential Equation! -Stuck!!-

    If [itex]b^x=b^y[/itex], then [itex]x=y[/itex]

    Remove [itex]b[/itex] from both sides, and you're left with something quite a bit easier to solve.
     
  7. Feb 7, 2010 #6

    Mark44

    Staff: Mentor

    Re: Exponential Equation! -Stuck!!-

    This is good advice, but the OP has already done this. Take a closer look at the original post.
     
  8. Feb 7, 2010 #7

    Mark44

    Staff: Mentor

    Re: Exponential Equation! -Stuck!!-

    2y + y and 2y2 are very different expressions. The first is (obviously) 2y + y, which is the same as 2y + 1y; the second is 2y*y.

    The distributive law says that a(b + c) = ab + ac, or equivalently, that (b + c)a = ba + ca. This second form looks a lot like 2y + 1y.
     
  9. Feb 7, 2010 #8
    Re: Exponential Equation! -Stuck!!-

    Ahh, sorry about that. I should have looked at the solution attempt more closely.
     
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