Results are out! Find what you need...fast. Get quick advice or join the chat
x

Unlock these great extras with your FREE membership

  • One-on-one advice about results day and Clearing
  • Free access to our personal statement wizard
  • Customise TSR to suit how you want to use it

Hard Logarithm Question

Announcements Posted on
Find your uni forum to get talking to other applicants, existing students and your future course-mates 27-07-2015
Win top prizes in our mega results day giveaway... 24-07-2015
  1. Offline

    ReputationRep:
    

(\log_3 p)^2 = \log_3(p^2)
    

\log_3(p+q)=\log_3 p + \log_3 q

    Solve these simultaneous equations.

    I've got  (\log_3 p)^2 = \log_3 (\frac{p^2 +qp}{q}) so far, but I don't know how to eliminate q.
  2. Offline

    ReputationRep:
    Solving the first equation gives you p, and then it's easy to find q from the 2nd.
  3. Offline

    ReputationRep:
    Ok thanks, got it.
  4. Offline

    ReputationRep:
    (Original post by Dan12)
    How do you find p?
    In the first equation, for the RHS, use the logarithmic identity that states that "the logarithm of the n-th power of a number is the same as n times the logarithm of the number." Then, treat the entire equation as a quadratic in log_3p (hint: substitute m=log_3p). Let me know if you still don't get it.
  5. Offline

    ReputationRep:
    Q1. (log3P)2 = log3(P2)
    (log3P)2 = 2(log3P)

    Let log3P = x

    x2 = 2x
    x = 2

    log3P = 2
    P = 9

    Q2. log3(P+Q) = log3P + log3Q
    log3(P+Q) = log3(PQ)
    P+Q = PQ

    Substitute P = 9 from Q1

    9+Q = 9Q
    9 = 8Q
    9/8 = Q
    Q= 1 1/8 or 1.125


    Therefore, P is 9 and Q is 1.25
  6. Offline

    ReputationRep:
    (Original post by 2012_jonathan_s)
    ...
    Welcome to TSR Jonathan.

    Two rules you should know.

    Don't bump old threads for no reason.

    Don't provide full solutions.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: November 18, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Do you think you'll do better or worse than your predicted grades?
New on TSR

Results are coming...

No sweat. Here's all you need to make sure you're ready

Study resources
x

Think you'll be in clearing or adjustment?

Hear direct from unis that want to talk to you

Get email alerts for university course places that match your subjects and grades. Just let us know what you're studying.

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.