Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By Plato
  • 1 Post By Soroban

Math Help - cos and natural log

  1. #1
    Junior Member
    Joined
    Mar 2012
    From
    San Francisco
    Posts
    32

    cos and natural log

    Find the smallest positive number 't' such that:
    10^(cos t) = 4

    Round answer to three decimal places.
    t = ? radians

    Thanks! =)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: cos and natural log

    Quote Originally Posted by jonathanraxa View Post
    Find the smallest positive number 't' such that:
    10^(cos t) = 4
    Round answer to three decimal places.
    t = ? radians
    t=\arccos\left(\frac{\ln(4)}{\ln(10)}\right)
    Thanks from jonathanraxa
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,685
    Thanks
    616

    Re: cos and natural log

    teHello, jonathanraxa!

    \text{Find the smallest positive number }t\text{ such that: }\,10^{\cos t} \,=\; 4
    \text{Round answer to three decimal places.}

    We have: . 10^{\cos t} \:=\:4

    \text{Take logs, base 10: }\;\log_{10}\!\left(10^{\cos t}\right) \;=\;\log_{10}\!4

    . . . . . . . . . . . . . \cos t\cdot\underbrace{\log_{10}10}_{\text{This is 1}} \;=\;\log4

    ,. . . . . . . . . . . . . . . . . . \cos t \;=\;\log4

    . . . . . . . . . . . . . . . . . . . . . t \;=\;\cos^{-1}\!\left(\log4\right)

    .
    Thanks from jonathanraxa
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: cos and natural log

    Quote Originally Posted by Soroban View Post
    teHello, jonathanraxa!

    . . . . . . . . . . . . . . . . . . . . . t \;=\;\cos^{-1}\!\left(\log4\right) .
    So as not to confuse the student it should be pointed out:
    \log_{10}(4)=\frac{\ln(4)}{\ln(10)}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Natural Map from R into End (M)
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: August 11th 2011, 04:00 AM
  2. natural log
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 13th 2011, 10:28 PM
  3. simplify natural log times natural log
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 3rd 2010, 09:31 PM
  4. natural log
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 1st 2009, 09:18 AM
  5. Natural log
    Posted in the Calculus Forum
    Replies: 8
    Last Post: May 1st 2008, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum