Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    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.
    Offline

    17
    ReputationRep:
    Solving the first equation gives you p, and then it's easy to find q from the 2nd.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ok thanks, got it.
    • PS Helper
    Offline

    0
    ReputationRep:
    PS Helper
    (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.
    Offline

    0
    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
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (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.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

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