Properties of Logarithms

Discussion in 'Other Pre-University Math' started by nycmathguy, Nov 6, 2021.

  1. nycmathguy

    nycmathguy

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    20211105_164308.jpg
     
    nycmathguy, Nov 6, 2021
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  2. nycmathguy

    MathLover1

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    f(x)=ln(1-1/x^2)


    f(2)+f(3)+f(4)=ln(5/8)

    f(2)=ln(1-1/2^2)=ln(1-1/4)=ln(3/4)
    f(3)=ln(1-1/3^2)=ln(1-1/9)=ln(8/9)
    f(4)=ln(1-1/4^2)=ln(1-1/16)=ln(15/16)

    f(2)+f(3)+f(4)=ln(3/4)+ln(8/9)+ln(15/16)

    f(2)+f(3)+f(4)=ln((3/4)(8/9)(15/16))
    f(2)+f(3)+f(4)=ln((3/4)(8/9)(15/16))...simplify
    f(2)+f(3)+f(4)=ln((1/4)(1/1)(5/2))
    f(2)+f(3)+f(4)=ln(5/(4*1*2))
    f(2)+f(3)+f(4)=ln(5/8) ->proven
     
    MathLover1, Nov 7, 2021
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Nice work like always.
     
    nycmathguy, Nov 7, 2021
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