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Math Help - Logarithmic Inequalities

  1. #1
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    Post Logarithmic Inequalities

    I am doing a lot of questions on logarithmic inequality but i am stuck at one question:-



    I dont from where to start.
    Please help.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Use that the inequality \log_3 y\geq 0 is equivalent to y\geq 1
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  3. #3
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    Quote Originally Posted by FernandoRevilla View Post
    Use that the inequality \log_3 y\geq 0 is equivalent to y\geq 1
    Thanks for your reply but i want to know how to get rid of modulus...
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    We have x^2+|x-5|>0 for all x\in\mathbb{R} so, the inequality is equivalent to |x^2-4x|+3\geq x^2+|x-5| . Now use the definition of the absolute value, |x-5|=x-5 if x>5 , ... etc.
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