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Math Help - Is this correct or should I use logs?

  1. #1
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    Is this correct or should I use logs?

    Hi did I simplify this correctly?
    (2^x+2^(x-1)) / (2^x+2^(x+1))
    Same base use multiplication rule

    2^x+x-1 / 2^x+x+1
    2^2x-1 / 2^2x+1
    Same base so use division rule
    2 ^ 2x-1 – (2x+1)
    2 ^ 2x-1 – 2x-1
    2 ^ -2
    =1/4
    Last edited by Neverquit; May 24th 2011 at 03:28 AM.
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  2. #2
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    It is hard to tell what that is supposed to be without more parentheses. My first guess was that you meant
    (2^x+ 2^(x-1))/(2^x+ 2^(x-1)) but that is equal to 1 because the numerator and denominator are the same.

    But then by the third step that "-1" in the denominator has mysteriously become "+1". Did you intend
    (2^x+ 2^(x-1))/(2^x+ 2^(x+1))?

    In any case, if the problem is either of those, you can't use a "multiplication rule" because you don't have a multiplication.
    It is true that (2^a)(2^b)= 2^(a+b) but you have 2^a+ 2^b, the sum, not the product.

    If it really is [tex]\frac{2^x+ 2^{x-1}}{2^x+ 2^{x+1}}[tex], I recommend you factor 2^(x- 1) out of the numerator and 2^x out of the denominator. That will give
    \frac{2^{x-1}(2+ 1)}{2^x(1+ 2)}
    Simplify that.
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  3. #3
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    put brackets in

    Sorry added brackets

    what I mean to state was 2 to the power of x plus 2 to the power of x minus one and that is all divided by 2 to the power of x plus 2 to the power of x plus 1.
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