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

[dagg3r]

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 don't 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 can't solve lol.



2. find the derivative of y=ln(t) * sin(t) i used the product rule and got
U=ln(x)
u`=1/x
V=sin(x)
v`=cos x
Dy/dx= ln(x)* cos(x) + sin(x)/x
if i let dy/dx=0 how do i solve for x?

 

[HallsofIvy]

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.

 

[dagg3r]

ok, thanks but there is another question that says algebracially is that the same as this?

y=0.5e^(0.1x)sin(t)

 

[Gza]

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