Results 1 to 2 of 2

Math Help - trignometry

  1. #1
    Member grgrsanjay's Avatar
    Joined
    May 2010
    From
    chennai,tamil nadu
    Posts
    143
    Thanks
    1

    Post trignometry

    solve the eqn:

    1/log(base 4) (x+1)/(x+2) < 1/log(base 4) (x+3)

    regret me
    the topic is LOGARITHMS
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,736
    Thanks
    642
    Hello, grgrsanjay!

    I have a very long solution . . . and it may be incomplete.
    Someone check it carefully . . . please!


    \text{Solve: }\;\dfrac{1}{\log_4\!\left(\frac{x+1}{x+2}\right)} \;<\; \dfrac{1}{\log_4(x+3)}\;\;[1]

    We begin with: . 1 \:<\:2

    Add x\!:\;\;x+1 \:<\:x+2\;\;[2]

    Domain: x \,>\,-1 \quad\Rightarrow\quad x+1 \,>\,0 \quad\Rightarrow\quad x+2 \,>\,0

    Divide [2] by positive x+2\!: . \dfrac{x+1}{x+2} \:<\:1

    Take logs, base 4: . \log_4\!\left(\dfrac{x+1}{x+2}\right)\:<\:\log_4(1  ) \:=\:0

    That is: . \log_4\!\left(\dfrac{x+1}{x+2}\right) .is negative.


    Multiply [1] by negative \log_4\!\left(\frac{x+1}{x+2}\right)\!: . 1 \;>\;\dfrac{\log_4\!\left(\frac{x+1}{x+2}\right)}{  \log_4(x+3)}\;\;[3]


    Since x \,>\, -1, then x+3 \,>\,2 \quad\Rightarrow\quad \log_4(x+3) \:>\:0


    Multiply [3] by positive \log_4(x+3)\!: . \log_4(x+3) \;>\;\log_4\!\left(\dfrac{x+1}{x+2}\right)

    Take anti-logs: . x+3\;>\;\dfrac{x+1}{x+2} \quad\Rightarrow\quad x^2 + 4x + 5 \;>\;0

    This is an up-opening parabola with its vertex at (-2, 1).
    . . Hence, it is always above the x-axis.


    The inequality is true for all x in the domain: . x \:>\:-1

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. trignometry
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 25th 2008, 10:26 AM
  2. Trignometry (sin law)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 27th 2008, 08:46 PM
  3. trignometry
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 8th 2008, 03:43 AM
  4. trignometry
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 7th 2008, 01:11 PM
  5. Trignometry (sin law & cos law)
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 3rd 2008, 08:52 PM

Search Tags


/mathhelpforum @mathhelpforum