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    Maths-
    General
    Easy

    Question

    The sum of all roots of sin invisible function application open parentheses pi log subscript 3 end subscript invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses close parentheses equals 0 inblank open parentheses 0 comma blank 2 pi close parentheses is

    1. 3 divided by 2  
    2. 4  
    3. 9 divided by 2  
    4. 13 divided by 3  

    The correct answer is: 9 divided by 2

      pi log subscript 3 end subscript invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals k pi comma blank k element of I
      log subscript 3 end subscript invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals k rightwards double arrow x equals 3 to the power of negative k end exponent
      The possible values of k are negative 1 comma blank 0 comma blank 1 comma blank 2 comma blank 3 comma blank horizontal ellipsis
      S equals 3 plus 1 plus fraction numerator 1 over denominator 3 end fraction plus fraction numerator 1 over denominator 3 to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 3 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity equals fraction numerator 3 over denominator 1 minus fraction numerator 1 over denominator 3 end fraction end fraction equals fraction numerator 9 over denominator 2 end fraction

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