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Math Help - Help on solving an equation

  1. #1
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    Help on solving an equation

    This is a question from the paper 1 of the last year's IB Math (HL) exam that my teacher gave out today.

    Q: Solve the equation 4^(x-1)=2^x+8.

    4^(x-1)=2^x+8
    4^x*4^(-1)=2^x+8
    4^(-1)=(1/2)^x+8/4^x
    4^(-1)=1/2^x+8/4^x

    Then I am stuck here.

    I do know that the answer is 3 but I need to know the steps and working that lead to the answer in order to obtain full marks on the exam. Some help will be really appreciated!
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  2. #2
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    4^x*4^(-1)=2^x+8
    Represent 4^x as (2^{x})^2.
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