1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Log Law Problems

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Write as a single logarithm:

    2. Relevant equations

    Logarithm Laws:

    [itex]log_a(xy) = log_a(x) + log_a(y)[/itex]

    [itex]log_a(\frac{x}{y}) = log_a(x) - log_a(y)[/itex]

    Problem Set:

    [itex]log_{10}A + log_{10}B - log_{10}C[/itex]

    [itex]\frac{1}{2}logX - 2log4[/itex]

    [itex]2logN + 3logX[/itex]

    3. The attempt at a solution

    I simplified the first question to [itex]log_{10}(\frac{AB}{C})[/itex] Am I correct?

    I wasn't sure about how to approach the second question. I multiplied [itex]\frac{1}{2}[/itex] by [itex]X[/itex] and [itex]2[/itex] by [itex]4[/itex] and simplified as follows:

    [itex]log_{10}{\frac{1}{2}X} - log_{10}8 [/itex]

    to get [itex]log_{10}(\frac{0.5x}{8})[/itex]

    I'm not sure if this is correct though.

    If it is wrong, how would I solve it correctly?

    For the third problem, I solved it to:

    [itex]log_{10}[ (2n)(3x) ][/itex]

  2. jcsd
  3. Oct 17, 2013 #2


    Staff: Mentor

    Your AB/C is correct.

    For the 1/2 log X you haven't listed the loglaw for it which is:

    C * log (x) = log (x^C)

    given that rework your answer.
  4. Oct 17, 2013 #3
    Yes..Thats right.

    That is not the correct way .

    Use the following property of logarithms : logb(xn) = n logbx.
  5. Oct 17, 2013 #4
    I solved the second one to:


    Is this correct?

  6. Oct 17, 2013 #5
  7. Oct 17, 2013 #6
    And would the second one be


  8. Oct 17, 2013 #7
  9. Oct 17, 2013 #8
    Thank you very much!
  10. Oct 17, 2013 #9


    Staff: Mentor

    dont forget to use the Thanks button to thank everyone.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted