Results 1 to 8 of 8

Math Help - Help with logarithms

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    7

    Help with logarithms

    So, you probably know that the formula for exponential growth is y=a(1+r)^t, with a being the original amount, r being the percent of growth, and t being the amount of time. I would like to learn to get t using logarithms.

    Hopefully you may be able to help. Thanks in advance!

    Gobblewobble123
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Start by taking the log of both sides, any base will do.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2011
    Posts
    7
    Maybe you could do a step by step example of how to solve for x using logs? I am trying to teach myself and I love examples! I'm not sure exactly what to do here, so anything helps.

    If I take the logs of both sides, would it look like this: log_10 {a(1+r)}=log_10 {y}?

    Your post is appreciated.

    Gobblewobble123
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2011
    Posts
    7
    Maybe you could do a step by step example on how to solve the problem? Examples are awesome!

    If I took the log of both sides, would it look like this: log_10 {a(1+r)}=log_10 {y}?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2011
    Posts
    7
    Maybe you could do a step by step example on how to solve the problem? Examples are awesome!

    If I took the log of both sides, would it look like this: \log_10 {a(1+r)}=\log_10 {y}?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2
    Quote Originally Posted by gobblewobble123 View Post
    So, you probably know that the formula for exponential growth is y=a(1+r)^t, with a being the original amount, r being the percent of growth, and t being the amount of time. I would like to learn to get t using logarithms.

    Hopefully you may be able to help. Thanks in advance!

    Gobblewobble123
    Since any base will do, I'll pick "e".
    ln(y) = ln[a(1 + r)^t] = ln(a) + t*ln(1 + r)
    ln(y) - ln(a) = t*ln(1 + r)
    ln(y/a) = t*ln(1 + r)
    ln(y/a)/ln(1 + r) = t
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293
    Quote Originally Posted by TheChaz View Post
    Since any base will do, I'll pick "e".
    ln(y) = ln[a(1 + r)^t] = ln(a) + t*ln(1 + r)
    ln(y) - ln(a) = t*ln(1 + r)
    ln(y/a) = t*ln(1 + r)
    ln(y/a)/ln(1 + r) = t
    It's easier if you divide both sides by a first, then take the logarithms, but it doesn't really make any difference.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member TheChaz's Avatar
    Joined
    Nov 2010
    From
    Northwest Arkansas
    Posts
    600
    Thanks
    2
    Quote Originally Posted by Prove It View Post
    It's easier if you divide both sides by a first, then take the logarithms, but it doesn't really make any difference.
    Funny - after having demonstrated this a few times to students today, I was so distracted by the notational difference (we use A = P(1 + r/n)^{nt}) that I skipped the first step!

    While the result is the same, I like to approach problems with invertible operations by composing their inverses (in reverse order), so dividing by a should have been first
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. logarithms help
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 6th 2010, 06:29 PM
  2. Logarithms
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 6th 2010, 04:46 PM
  3. logarithms
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 24th 2010, 04:26 AM
  4. Logarithms
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 18th 2010, 02:52 PM
  5. logarithms
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 16th 2008, 09:55 AM

Search Tags


/mathhelpforum @mathhelpforum