Results 1 to 2 of 2

Math Help - Two Exponential Equations, and Two Triq Questions!

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    9

    Two Exponential Equations, and Two Triq Questions!

    1. 9^x+4*3^x - 3 = 0

    2. 5^x = 4^x+5 <-----its 4^x+5, 4 is raised to the x+5!!! Can't figure out how to make it look that way.. =/

    3. A formula for cos(3X) in terms of cosX alone.

    4. The period of 3cos(5pix+7)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    _______________________________________

    #1:

    \begin{aligned}9^x + 4 \cdot 3^x - 3 & = 0 \\ \left(3^2\right)^x + 4 \cdot 3^x - 3 & = 0 \\ \left(3^x\right)^2 + 4 \cdot 3^x - 3 & = 0 \end{aligned}

    If it helps, imagine y = 3^x. Then we get an easier problem: y^2 + 4y - 3 = 0

    _______________________________________

    #2: Start by taking the natural logarithm of both sides ..

    \begin{aligned} {\color{red}\ln \ }5^x & = {\color{red}\ln \ }4^{x+5} \\ x \ln 5 & = (x+5) \ln 4 \qquad \text{ Since: } \ln a^b = b\ln a\\ & \ \ \vdots \end{aligned}

    _______________________________________

    #3: \cos (3x) = \cos (x + 2x)

    Now these will come in handy:
    • \cos (a + b) = \cos a \cos b - \sin a \sin b
    • \cos (2a) = 2\cos^2 a - 1
    • \sin (2a) = 2\sin a \cos a
    • \sin^2 (a) = 1 - \cos^2 a


    _______________________________________

    #4: 3\cos \left(5\pi x + 7\right) \ = \ 3\cos \left( 5\pi \left(x + \frac{7}{5\pi}\right)\right)

    If you remember, if you have a sinusoidal wave in the form: y = A\cos (B (x + C)) + D

    The period is given by: \frac{2\pi}{B}

    _______________________________________
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Small question about triq equations
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: April 10th 2010, 07:36 AM
  2. Exponential equations questions
    Posted in the Algebra Forum
    Replies: 9
    Last Post: December 6th 2009, 08:10 PM
  3. Solving triq equations
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 14th 2009, 05:48 AM
  4. Can I get help with this triq problem?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: June 9th 2008, 06:27 PM
  5. triq eqautions
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 17th 2008, 05:54 AM

Search Tags


/mathhelpforum @mathhelpforum