Advertise on Bikeforums.net



User Tag List

Results 1 to 19 of 19

Thread: Logarithm

  1. #1
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)

    Logarithm



    To solve for x I thought I would rewrite the equation in exponential form:

    3^(2-x) = 3

    Anything raised to the power of 1 is itself. So, x must equal 1. Because 3^(2-1) = 3

    Why is this incorrect?
    C://dos
    C://dos.run
    run.dos.run

  2. #2
    Lucky 47 crash66's Avatar
    Join Date
    Oct 2004
    Location
    The past
    My Bikes
    2005 Specialized Allez Elite
    Posts
    283
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by phantomcow2 View Post


    To solve for x I thought I would rewrite the equation in exponential form:

    3^(2-x) = 3

    Anything raised to the power of 1 is itself. So, x must equal 1. Because 3^(2-1) = 3

    Why is this incorrect?

    You're lucky so many people here like to show off their mad math skillz, otherwise you'd have spent a fortune on tutoring by now.
    Has anyone else noticed that 47 is a magic number?

  3. #3
    L T X B O M P F A N S R apricissimus's Avatar
    Join Date
    Jun 2008
    Location
    Melrose, MA
    My Bikes
    Bianchi Volpe, Bianchi San Jose, Redline 925
    Posts
    2,226
    Mentioned
    3 Post(s)
    Tagged
    0 Thread(s)
    log_3(2 - x) = 3

    3^log_3(2 - x) = 3^3

    2 - x = 9

    x = -7
    Last edited by apricissimus; 08-03-08 at 05:19 PM.

  4. #4
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    I actually solved that a short bit ago. Thanks though.
    C://dos
    C://dos.run
    run.dos.run

  5. #5
    Senior Member deraltekluge's Avatar
    Join Date
    Sep 2006
    My Bikes
    Kona Cinder Cone, Sun EZ-3 AX
    Posts
    1,195
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Uh...3³ is not 9. It's 27.

  6. #6
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by deraltekluge View Post
    Uh...3³ is not 9. It's 27.
    I now realize that. THanks
    C://dos
    C://dos.run
    run.dos.run

  7. #7
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Okay okay, now how about this:


    The best I can do is rewrite it as .5xLog(.7) = 5log(1-x)
    C://dos
    C://dos.run
    run.dos.run

  8. #8
    trois, mon frère JaRow's Avatar
    Join Date
    Jan 2008
    Location
    Gainesville/Miami, FL
    My Bikes
    '01 Gary Fisher Wahoo, '08 Giant TCR C2
    Posts
    576
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Is this your math hw?

  9. #9
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Yes, and let me write my disclaimer now:

    I seek guidance only, not the answer.
    C://dos
    C://dos.run
    run.dos.run

  10. #10
    Hazardous Taerom's Avatar
    Join Date
    Jun 2005
    Location
    Quarantine
    My Bikes
    2005 Trek Liquid 55, 2009 Haro Mary SS
    Posts
    727
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Just plug it into your calculator's numeric solver and be done with it.

  11. #11
    Senior Member deraltekluge's Avatar
    Join Date
    Sep 2006
    My Bikes
    Kona Cinder Cone, Sun EZ-3 AX
    Posts
    1,195
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    That's not correct. You did the left side of the equation correctly, but you got things backwards on the right side.

    Remember, log(x^y) = y* log(x)

  12. #12
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by Taerom View Post
    Just plug it into your calculator's numeric solver and be done with it.
    That's what made me mathematically handicapped in the first place!
    C://dos
    C://dos.run
    run.dos.run

  13. #13
    L T X B O M P F A N S R apricissimus's Avatar
    Join Date
    Jun 2008
    Location
    Melrose, MA
    My Bikes
    Bianchi Volpe, Bianchi San Jose, Redline 925
    Posts
    2,226
    Mentioned
    3 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by deraltekluge View Post
    Uh...3³ is not 9. It's 27.
    *slaps palm on forehead*

    I'm actually a math editor in real life. Minus a million points for me.
    Last edited by apricissimus; 08-03-08 at 06:40 PM.

  14. #14
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Oh, so I should have

    .5xlog(.7) = 1-xlog(5)

    then divide by log5 on both sides to begin isolation of the variable?
    C://dos
    C://dos.run
    run.dos.run

  15. #15
    Senior Member deraltekluge's Avatar
    Join Date
    Sep 2006
    My Bikes
    Kona Cinder Cone, Sun EZ-3 AX
    Posts
    1,195
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by phantomcow2 View Post
    Oh, so I should have

    .5xlog(.7) = 1-xlog(5)

    then divide by log5 on both sides to begin isolation of the variable?
    Remember that it's (1-x). Make sure you keep your parentheses arranged properly.

  16. #16
    trois, mon frère JaRow's Avatar
    Join Date
    Jan 2008
    Location
    Gainesville/Miami, FL
    My Bikes
    '01 Gary Fisher Wahoo, '08 Giant TCR C2
    Posts
    576
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by phantomcow2 View Post
    Yes, and let me write my disclaimer now:

    I seek guidance only, not the answer.
    I'm not faulting you for it. It's a shame more people aren't this proactive about their education.
    Last edited by JaRow; 08-03-08 at 07:07 PM. Reason: bad spelling mistake

  17. #17
    L T X B O M P F A N S R apricissimus's Avatar
    Join Date
    Jun 2008
    Location
    Melrose, MA
    My Bikes
    Bianchi Volpe, Bianchi San Jose, Redline 925
    Posts
    2,226
    Mentioned
    3 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by phantomcow2 View Post
    Okay okay, now how about this:


    The best I can do is rewrite it as .5xLog(.7) = 5log(1-x)
    By some algebraic manipulation, you can rewrite the equation as (35/2)^x = 5^2. (Try to do it yourself.)

    From here take the log (to a certain base b) of both sides, and use the change of base formula, log_b(x) = log_a(x)/log_a(b) (or ln(x)/ln(b) if you like natural logarithms. And who doesn't?).

  18. #18
    la vache fantôme phantomcow2's Avatar
    Join Date
    Aug 2004
    Location
    NH
    Posts
    6,266
    Mentioned
    0 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by apricissimus View Post
    By some algebraic manipulation, you can rewrite the equation as (35/2)^x = 5^2. (Try to do it yourself.)

    From here take the log (to a certain base b) of both sides, and use the change of base formula, log_b(x) = log_a(x)/log_a(b) (or ln(x)/ln(b) if you like natural logarithms. And who doesn't?).
    And as usual, it's the algebraic manipulation which sinks me.
    C://dos
    C://dos.run
    run.dos.run

  19. #19
    L T X B O M P F A N S R apricissimus's Avatar
    Join Date
    Jun 2008
    Location
    Melrose, MA
    My Bikes
    Bianchi Volpe, Bianchi San Jose, Redline 925
    Posts
    2,226
    Mentioned
    3 Post(s)
    Tagged
    0 Thread(s)
    Quote Originally Posted by phantomcow2 View Post
    And as usual, it's the algebraic manipulation which sinks me.
    Here's the first couple of steps:

    Rewrite as

    (0.7^x)^1/2 = 5*(5^(-x))

    Then square both sides...

    0.7^x = (5^2)*(5^(-2x))

    etc.

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •