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How to solve a hard question involving multiplication of ln(t) and sin(t)

  1. May 24, 2004 #1
    hi guys,
    this is a question i got really confused on

    they give you a question which is 3=ln(t) * sin(t)

    solve for t. i dont know how to do this algebracially if it is even possible. i can do it on my calculator by sketching the graph and finding the exact value but how do you do this algebracially?.

    The best i can get is ln(t) = 3/sin(t) but still i cant solve lol.

    2. find the derivative of y=ln(t) * sin(t) i used the product rule and got
    v`=cos x
    Dy/dx= ln(x)* cos(x) + sin(x)/x
    if i let dy/dx=0 how do i solve for x?
    Last edited: May 24, 2004
  2. jcsd
  3. May 24, 2004 #2


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    Staff Emeritus
    Science Advisor

    ln(t) and sin(t) are both "transcendental" functions and, in general, there is no algebraic way to get an exact value. You can, as you say, use a graphing calculator to get an approximate (not exact) value for t. The equation 3= ln(t)*sin(t) has an infinite number of solutions but I get approximately x= 20.3 for the smallest.

    As for problem 2, yes, dy/dx= ln(x)* cos(x) + sin(x)/x. Again, there is no algebraic way to get an exact solution to dy/dx= 0. You could again get an approximate solution using a graphing calculator. Once again, there are an infinite number of solutions and I find the smallest to be about x= 0.35.
    By the way, why do you want to solve that equation? The problem as you stated it only asked you to find the derivative and you have done that.
  4. May 24, 2004 #3
    ok, thanks but there is another question that says algebracially is that the same as this?

  5. May 29, 2004 #4


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    perhaps Euler's famous equation may be of some service?
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