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!

Am I wrong ? log question

  1. Apr 19, 2013 #1
    1. The problem statement, all variables and given/known data
    2log2 x - log2 (x-3) = 2





    The attempt at a solution

    So what I did was , expand the brackets

    2log x - logx + log3 = 2

    logx = 2-log3

    logx = log 4 - log 3

    log x = log ( 4-3)

    x= 4/3?

    Is this right?
     
  2. jcsd
  3. Apr 19, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    No, it's wrong. log(a-b) is not equal to log(a)-log(b). Try taking 2 to the power of each side of your original equation.
     
  4. Apr 19, 2013 #3
    Aww got that wrong on my test then ;((

    Okay how about this?

    log x^2 / (x-3) = log 4

    removing logs

    x^2/(x-3) = 16
    16x-48 = x^2

    x^2 -16x + 48=0
    (x -4 )(x -12)
     
    Last edited: Apr 19, 2013
  5. Apr 19, 2013 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What you get after 'removing logs' would be fine if your original equation were 2log(x)-log(x-3)=4 since 4=log(16). Was it?
     
  6. Apr 19, 2013 #5

    Mark44

    Staff: Mentor

    This is wrong, too, right in your first step. I should add that what you wrote is probably not what you meant. This is how the left side would be interpreted:
    $$ \frac{log x^2}{x - 3}$$

    From your subsequent work, I think this is what you meant:
    $$ log(\frac{x^2}{x - 3})$$

    If so, when you write it in plain text (as opposed to LaTeX) add parentheses, like this
    log(x2/(x - 3))

    Where you headed in your first step uses the idea that if log A = log B, then A = B.
    Applying that idea, you get x2/(x - 3) on the left side. What do you get on the right side? Hint: NOT 16.
     
  7. Apr 20, 2013 #6
    log(x^2/(x-3)) = log 4

    (x^2/(x-3)) = 4?
     
  8. Apr 20, 2013 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted