C2 log question...

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Please change your TSR password 23-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
Search Thread
Advanced Search
Sign in to Reply
  1. studentccs's Avatar
    1 22-05-2012  11:57
    • Full Member
    • Posts: 128
    C2 log question...
    Solve the simultaneous equations:
    Log2(x)+Log8(y)=-1
    Log4(x)+Log2(y)=2

    All logs here are to the base, ie not Log 2x
    Please help
  2. JJMills's Avatar
    2 22-05-2012  12:42
    • Full Member
    • Location: Wiltshire
    • Posts: 95
    Re: C2 log question...
    Before I go into it, have you got a value of x and y so I can check I'm right?

    Edit:

    I managed to get an answer that works for both of your values. Pretty sure I've never done anything like this for C2 though, what exam board are you with? Also, how many marks was this question?

    To do this question you need to use pretty much all the rules for logs you know. Using log_a x = \frac {log_b x}{log_b a} to give them all the same base and b*log_a x = log_a x^b, log_a x + log_a y = log_a xy and log_a x - log_a y = log_a \frac {x}{y} to simplify the equations.

    I'd advise you have another got at this before you look at my workings. Make sure you put them all in the same base for ease and then manipulate the equations to get values for x and y.

    Spoiler:
    Show

    log_2 x + log_8 y = -1 = -log_2 2 = log_2 2^{-1} log_4 x + log_2 y = 2 = 2 \times log_2 2 = log_2 2^2 log_8 y = \frac {log_2 y}{log_2 8} = \frac {log_2 y}{log_2 2^3} = \frac {log_2 y}{3} log_4 x = \frac {log_2 x}{log_2 4} = \frac {log_2 x}{log_2 2^2} = \frac {log_2 x}{2} log_2 x + \frac {log_2 y}{3} = log_2 2^{-1} 3 \times log_2 x + log_2 y = 3 \times log_2 2^{-1} = log_2 2^{-3} = log_2 x^3 + log_2 y ((log_2 x) \div 2) + log_2 y = log_2 2^2 log_2 x + 2 \times log_2 y = 2 \times log_2 2^2 = log_2 2^4 = log_2 x + log_2 y^2 log_2 (x^3 \times y) = log_2 2^{-3} log_2 (x \times y^2) = log_2 2^4 xy^2 = 2^4 x = 2^4 \div y^2 x^3y = 2^{-3}
    (2^4 \div y^2)^3 \times y = 2^{-3} 2^{12} \div y^6 \times y = 1 \div 8 2^{12} = y^5 \div 8 2^{15} = y^5 y = 8 x \times y^2 = 2^4 64x = 2^4 x = 0.25
    Last edited by JJMills; 22-05-2012 at 14:08.
  3. the bear's Avatar
    3 22-05-2012  14:03
    • TSR Demigod
    • Location: Linton Travel Tavern
    • Posts: 7,200
    Re: C2 log question...
    you need to do something like replace log2y with 3log8y

    and log2x with 2log4x
  4. raheem94's Avatar
    4 22-05-2012  14:04
    • TSR Demigod
    • Posts: 5,512
    Re: C2 log question...
    (Original post by studentccs)
    Solve the simultaneous equations:
    Log2(x)+Log8(y)=-1
    Log4(x)+Log2(y)=2

    All logs here are to the base, ie not Log 2x
    Please help
    You need to use the change of base rule.

    \displaystyle log_2 x + log_8 y = -1 \implies log_2 x + \frac{log_2 y}{log_2 8} = -1 \implies log_2 x + \frac{log_2 y}{3} = -1 \\ \implies x^3 y = \frac18

    In a similar way construct an equation using log_4 x + log_2 y = 2

    Then sub one equation into another to find the values.
Sign in to Reply
Search Thread
Advanced Search
Share this discussion:  
Useful resources

Articles:

Study Help rules and posting guidelinesStudy Help Member of the Month nominationsGuide to MathematicsMathematics resourcesMathematics websitesMathematics revision notes in the TSR wikiCambridge Assessment admissions tests (including STEP)How to use LaTeXCareers in Mathematics

Useful Dates:

Quick Link:

Unanswered Maths Threads

Groups associated with this forum:

View associated groups
Article updates
Moderators

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

This forum is moderated by:

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

Shortcuts

Get Started

TSR Group

Using TSR

Info

Connect with TSR

Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.