Change-of-Base Formula

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 19, 2021.

  1. nycmathguy

    nycmathguy

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    Section 3.3
    10 & 12

    20211018_194022.jpg

    Question 10

    log 12/log 0.4 = -2.7119194414

    Answer: -2.712

    Question 12

    log 0.125/log (2/3) = 5.1285338747

    Answer: 5.129
     
    nycmathguy, Oct 19, 2021
    #1
  2. nycmathguy

    MathLover1

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    correct
    but, you need to do steps

    log(0.4,12) ->to base 10
    log(12)/log(0.4)..............write 12 as 3*4 and 0.4 as 4/10

    log(3*4)/log(4/10)

    apply log rules: log(xy)=log(x)+log(y) and log(x/y)=log(x)-log(y)

    (log(3)+log(4))/(log(4)-log(10)).......log(10)=1 and log(4)=log(2^2)=2log(2)
    (log(3)+2log(2))/(2log(2)-1)=-2.7119194414
     
    MathLover1, Oct 19, 2021
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    I get it. Steps have to be shown along the way.
     
    nycmathguy, Oct 19, 2021
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