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Math Help - Inequality with logarithm help needed.

  1. #1
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    Inequality with logarithm help needed.

    The question is
    log2(x+1)≤3


    then a<x≤b.


    What are a and b?


    How do I solve this?


    I can solve for b which is 7. But how do I solve for a?
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  2. #2
    Moo
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    Hello,

    The logarithm (in any base) is defined only over (0,\infty)

    So 1+x has to be > 0
    This makes x>-1 (a=-1)

    Then, we know that the logarithm is an increasing function.
    So \log_2(1+x)\leq 3 \Leftrightarrow 1+x \leq 2^3

    so b=...
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  3. #3
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    Thanks.
    I didn't know that.
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