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Complex Logarithmic questions

  1. Nov 6, 2012 #1
    1. The problem statement, all variables and given/known data

    A) Solve LogX^(LogX) = 4
    B) Log3 X - Log27 X = 4/3

    2. Relevant equations

    Basic 3 log rules: 1. Logc(MN) = LogcM + logcN 2. Logc(M/N) = LogcM - LogcN 3. LogcM^p = pLogcM

    3. The attempt at a solution
    I have no idea how to start either.
    Last edited: Nov 6, 2012
  2. jcsd
  3. Nov 6, 2012 #2


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    Find the "Relevant equations" for part 2 of the format.

    What is or are the bases for question #B ? Also, what is or are the bases for #A?

    Take care of those, and helping you will be easier; otherwise your problem description and question are not understandable.

  4. Nov 6, 2012 #3
    For part A) the base is 10, therefor thats why it isnt written, and for B it's the 3 and 27.
  5. Nov 6, 2012 #4


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    You still need to decide which relevant equations or properties you need for part 2 of the format template. One of them should be the change of base formula for question #B.
  6. Nov 7, 2012 #5
    Those are the only log formulas I know and have learned. This is an extend question.
  7. Nov 7, 2012 #6


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    If you have a log(x)^(anything) what do you get?
  8. Nov 7, 2012 #7


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    You know the relation following from definition of logarithm:
    [tex]a ^{log_a(x)}=x[/tex]

    Apply to the base 27 logarithm:

    [tex]27 ^{log_{27}(x)}=x[/tex]

    Take the base 3 logarithm of both sides: you find how log27(x) is related to log3(x).

  9. Nov 7, 2012 #8


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    I assume that A) is:
    Solve [itex]\displaystyle \log\left(x^{\log(x)}\right)=4\ ,\ \ [/itex] of course that is a base 10 logarithm, as you noted elsewhere.​
    Use the [itex]\displaystyle \log_{\,c}\left(x^{p}\right)=p\,\log_{\,c}(x)\ \ [/itex] property on A).

    Have you learned the change of base formula? Use it for B).
  10. Nov 7, 2012 #9
    There is one more property that you can make use of here,
    [tex]log_{a^c} b=\frac{log_a b}{c}[/tex]
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