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Math Help - Indicies Problem

  1. #1
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    Indicies Problem

    I am asked to show that: 2^(x+1) + 2^(x-1) = 160 can be written as 2.5 * (2^x) =160

    Could somebody please show me the steps taken to do this simplification? Since there is an addition, I can't get the rules of indicies to help me. In other questions like this I have always been able to use substitution/factorisation but i can't see a common factor.

    Thanks for your help.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by StaryNight View Post
    I am asked to show that: 2^(x+1) + 2^(x-1) = 160 can be written as 2.5 * (2^x) =160

    Could somebody please show me the steps taken to do this simplification? Since there is an addition, I can't get the rules of indicies to help me. In other questions like this I have always been able to use substitution/factorisation but i can't see a common factor.

    Thanks for your help.
    2^{x+1} + 2^{x-1} = 160

    2^x 2^1 + 2^x 2^{-1} = 160

    2^x \left( 2 + \frac{1}{2} \right) = 160

    2^x \left( \frac{5}{2} \right) = 160
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