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Completely expand as a sum/difference of logs

  1. Oct 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Completely expand as a sum/difference of logs
    log [ ( 2x^4(x-15)^3) / (12 sqrt (x^4-16) ]

    2. Relevant equations

    3. The attempt at a solution

    log 2x^4(x-15)^3 - log 12 sqrt (x^4-16)
    3 log 2x^4(x-15) - 1/2log 12 (x^4-16)
    Last edited: Oct 13, 2013
  2. jcsd
  3. Oct 13, 2013 #2


    Staff: Mentor

    Some clarification, please. The numerator of what you wrote is
    2x4 * (x - 15)3.

    If that isn't what you meant, please use parentheses or brackets to make it clearer.
    Some parentheses would make this more readable, as would the inclusion of = for things that are equal.

    Also, sqrt(x) = x1/2, not x1/3.
  4. Oct 13, 2013 #3
    1) yeah, that's what i meant to say, but i didn't know how to do the exponents

    2) ok okay thanks! did I solve the problem right because i'm not very sure :\
  5. Oct 13, 2013 #4


    Staff: Mentor

    Starting here --
    log [ ( 2x^4 * (x-15)^3) / (12 sqrt (x^4-16) ]
    = log [ 2x^4 * (x-15)^3] - log[12 * (x^4-16)^(1/2)]
    Can you continue?

    Notice that I added * to indicate multiplication. I think that's what you intended, but am not sure.

    There are some properties of logs that you either don't know or aren't using, such as log(AB) = log(A) + log(B), assuming both A and B are positive.
  6. Oct 13, 2013 #5
    after continuing would it be:

    [log 2x^4 + log (x-15)^3] - [log 12 + log (x^4-16)^1/2]

    and then use the power rule?

    [4 log 2x + 3 log (x-15)] - [log 12 + 1/2 log (x^4-16)]
  7. Oct 13, 2013 #6


    User Avatar
    Homework Helper
    Gold Member

    It's still not completely expanded.
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