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Can I use brackets on the subscript of a log?

  1. Jun 18, 2012 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution


    Hi, can I type brackets around the subscript of a log? Can I type brackets around the non subscript as well?

    I included what I mean in the picture below, as it's maybe easier to see what I mean. I'm just concerned that the meaning of what I wrote changes when I include the brackets. I don't want it to now mean multiplied where it shouldn't.


    Do both forms mean the same thing? Thanks
     

    Attached Files:

  2. jcsd
  3. Jun 18, 2012 #2

    Mentallic

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    I wouldn't bother with the brackets, just make sure that if you're writing out the subscripts on paper that it's obvious which is which.

    By the way, take a look at this proof:

    [tex]\log_ab=x[/tex]
    This is equivalent to
    [tex]a^x=b[/tex]
    Now, the LHS can become
    [tex]\frac{1}{a^{-x}}=\left(\frac{1}{a}\right)^{-x}[/tex]
    Hence we can use the definition of the log again to transform it back into
    [tex]\log_{1/a}b=-x[/tex]

    :wink:
     
  4. Jun 18, 2012 #3
    Sorry, but why did you include that? I'm just confused. I appreciate it though.

    Anyway, I'd like to use the brackets if possible, just because when I write my calculations in Word, a subscript '1/3' looks kind of weird to me, because it doesn't look like 1 over 3.

    Thanks
     
  5. Jun 18, 2012 #4

    LCKurtz

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    The parentheses won't hurt anything. Go ahead and use them.
     
  6. Jun 18, 2012 #5

    Mentallic

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    Because if [tex]\log_ab=x[/tex] and [tex]\log_{1/a}b=-x[/tex] then [tex]\log_{1/a}b=-\log_ab[/tex] hence you can change your log expressions from [itex]\log_{1/7}3[/itex] to [itex]-\log_73[/itex]
     
  7. Jun 18, 2012 #6
    Oh great, thanks to both of you.
     
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