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Math Help - Having trouble solving for n in the expontents place with uncommon base.

  1. #1
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    Having trouble solving for n in the expontents place with uncommon base.

    I have the equation:

    16^n < 8^(n+1)

    And need to solve for n.

    What I did:

    8^(4/3) = 16

    n < (4/3)(n+1)
    n < 4/3n + 4/3
    3n < 4n + 4
    -n < 4
    n > 4

    But, in the back of the book the answer is n < 3. What did I do wrong?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by thyrgle View Post
    I have the equation:

    16^n < 8^(n+1)

    And need to solve for n.

    What I did:

    8^(4/3) = 16

    n < (4/3)(n+1)
    n < 4/3n + 4/3
    3n < 4n + 4
    -n < 4
    n > 4

    But, in the back of the book the answer is n < 3. What did I do wrong?
    Your claim is correct: 8^{4/3} =16. So that implies that the inequality can be written as:

    (8^{4/3})^n < 8^{n+1}\implies 8^{4n/3}<8^{n+1}

    So this is true when \frac{4}{3}n<n+1 and this will give you the conclusion that's desired ( n<3).

    I hope this clarifies things.
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  3. #3
    Junior Member
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    Ok thanks, I switched them around, my brain is dead today.
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