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Math Help - Logarithm

  1. #1
    Junior Member darence's Avatar
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    Logarithm

    One more problem:

    Find all k \in R so that inequalities log_{(x-1)^2}(x+5)^4\geq1 and log_{x+k}(x+3)\leq1 have no mutual solutions.
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  2. #2
    MHF Contributor
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    Re: Logarithm

    Hey darence.

    Can you show us what you have tried (Hint: try expanding the definitions using log laws for change of base and powers and get an expression with k on one side of the inequality)?
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  3. #3
    Junior Member darence's Avatar
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    Re: Logarithm

    That's my biggest problem. I don't know where to start from with this problem
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  4. #4
    MHF Contributor
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    Re: Logarithm

    Hint: log_a(x) = ln(x)/ln(a) [Change of Base Rule] and ln(a^x) = x*ln(a)
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