Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    ok i think im bein abit thick but i keep gettin the wrong answer

    solve the equation 3^2x=4^2-x

    thanks!
    Offline

    0
    ReputationRep:
    do u mean 4^2 - x or 4^(2-x)?
    Offline

    16
    ReputationRep:
    ok i think im bein abit thick but i keep gettin the wrong answer

    solve the equation 3^2x=4^2-x

    thanks!

    2xlog3 = 2-xlog4
    2xlog3 - (2-xlog4) = 0
    sry im tired i can't think

    factorise that by taking x as a common letter you will get x( something something) Thus you can solve for x, i think that's how you do it. I haven't completed my c2 logs bit yet.
    Offline

    0
    ReputationRep:
    2xlog3 = 2-xlog4
    2x/2-x = log4/log3

    but then thats difficult to find x from there
    Offline

    0
    ReputationRep:
    (Original post by madhapper)
    2xlog3 = 2-xlog4
    2x/2-x = log4/log3

    but then thats difficult to find x from there
    if thats true then
    log4/log3 = 1.26...

    2x/(2-x) = 1.26...
    2x = (2-x)1.26
    2x = 2.52...-1.26..x
    2x - 1.26x = 2.52
    0.73x = 2.52..
    x = 2.52/0.73
    x = 3.419022...

    or
    x = 2(log4/log3)/(2 - [log4/log3])
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by manps)
    if thats true then
    log4/log3 = 1.26...

    2x/(2-x) = 1.26...
    2x = (2-x)1.26
    2x = 2.52...-1.26..x
    2x - 1.26x = 2.52
    0.73x = 2.52..
    x = 2.52/0.73
    x = 3.419022...

    or
    x = 2(log4/log3)/(2 - [log4/log3])
    the answer is 0.774
    ???????????????
    Offline

    16
    ReputationRep:
    try my method :P
    another method..
    3^2x=4^2-x

    take logs to the base 3 of each side
    you will get [logs are to the base 3 here]
    2x = (2-x)log4
    2x / (2-x) = log 4

    or take logs to the base 4
    2xlog3 = 2-x
    2-x / 2x = log 9 + log 3x
    Therefore: 6x^2 - (2-x) = -log9

    6x^2 - 2 - x + log 9 = 0

    I give up
    Offline

    0
    ReputationRep:
    i got ur answer

    3^2x = 4^(2-x)
    2x.log3 = (2-x).log4
    log3/log4 = (2-x)/(2x)
    0.79248.... = (2-x)/(2x)
    1.584962501x = 2-x
    2.584962501x = 2
    x = 2/2.584962501
    x = 0.774 (3dp)
    Offline

    14
    ReputationRep:
    3^2x=4^2-x
    2xln3=(2-x)ln4
    2xln3+xln4=2ln4
    x(2ln3+ln4)=2ln4
    x = 2ln4/(2ln3+ln4)

    but i dont have a calculator to check that
    Offline

    14
    ReputationRep:
    nas you want to take logs to the base 10 usually, so your calculator can do it
    Offline

    16
    ReputationRep:
    v.true. However, i didnt think sarah liked my method with lg, log to the base 3 and 4 makes gets rid of the nasty bits of the equation. Just thinking maybe something may come out of it which would solve the question.. unlucky though
    Offline

    12
    ReputationRep:
    (Original post by sarah12345)
    solve 3^(2x)=4^(2-x)
    3^(2x) = 4^(2-x)
    ---> 2xln3 = (2-x)ln4
    ---> 2x/(2-x) = ln4/ln3
    ---> (2xln3)/(ln4) = 2-x
    ---> x(2ln3/ln4) = 2-x
    ---> (2-x)/x = ln9/ln4
    ---> 2/x - 1 = ln9/ln4
    ---> 2/x = (ln9/ln4) + 1
    ---> x/2 = 1/[(ln9/ln4) + 1]
    ---> x = 2/[(ln9/ln4) + 1]
    ---> x = 0.774 (3.S.F)
 
 
 

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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

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.