precalc

(-2)^x = - 1/128

solve for x

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asked by tom
  1. does x=-7?

    1. 👍 0
    2. 👎 0
    posted by tom
  2. yes

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    2. 👎 0
    posted by Steve
  3. Your answer is correct.


    ( - 2 )ˣ = - 1 / 128

    Multiply both sides by 128


    128∙( - 2 )ˣ = - 1

    Raise both sides to the power 2

    128²∙[ ( - 2 )² ]ˣ = ( - 1 )²


    128 = 2⁷ , ( - 2 )² = ( 2 )² , so:

    (2⁷)²∙(2²)ˣ = 1

    _______________________________
    Remark:

    (2⁷)² is the same (2²)⁷
    ___________________________


    (2²)⁷∙(2²)ˣ = 1

    4⁷∙4ˣ = 1

    _____________________
    Remark:

    nᵃ∙ nᵇ = nᵃ⁺ᵇ

    Any number raised to the powe zero is one.

    So:

    4⁷ ∙ 4ˣ = 4⁷⁺ˣ

    4⁰ = 1
    _____________________

    4⁷⁺ˣ = 4⁰

    Take the logarithms base 4 of both sides

    log₄( 4⁷⁺ˣ ) = log₄( 4⁰ )

    _______________________________________
    Remark:

    log aᵐ = m ∙ log a

    log₄( 4 ) = 1

    So:

    log₄( 4⁷⁺ˣ ) = ( 7 + x ) ∙ log₄ ( 4 ) = ( 7 + x ) ∙ 1 = 7 + x

    log₄= 4⁰ = 0 ∙ log₄( 4 ) = 0
    _______________________________________

    7 + x = 0

    Subtract 7 to both sides

    7 + x - 7 = 0 - 7

    x = - 7

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    posted by Bosnian
  4. whoa! Can you say overkill??

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    posted by Steve
  5. Steve

    solve for x mean SOLVE for x


    Just say:

    x = - 7 is not enough.

    I showed the way to the solution.

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    posted by Bosnian

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