Homework Help: Log question

1. Oct 30, 2005

dragon513

Hi, this should be the last question for today :lol:
Determine the number of solutions for the following system:
$$y = -4log_{12} (x)$$
$$y = 4 sin(x)$$
Is there a way to do this without using a graphing calculator? Thank you very much!

Last edited: Oct 30, 2005
2. Oct 30, 2005

Tide

You do know that -1 <= sin(x) <= 1. That should be a good place to start. :)

3. Oct 31, 2005

PhysicsinCalifornia

Hi, hopefully you know some properties of log for the first one.
Hint:$$y=log_{10}(x)$$
$$10^y = x$$
and $$y=a*logx = log(x^a)$$

For the second one, what do you have trouble with?
Can you draw $$y=sinx$$?(of course without a calculator)
If you CAN, 4 is just the amplitude, and the graph's domain is$$(-\infty, \infty)$$

4. Oct 31, 2005

dragon513

Thanks for the input, but that's how far I got by myself :(
I should I get the intersecting points of the two graphs? Should I just use the calculator? Or is there another way around it?

5. Oct 31, 2005

ivybond

You don't need to "get the intersecting points of the two graphs", you want to find their number.
Helpful apprach - solve an easier problem first:
how many points of intersection do these graphs have
$$y=4 sin(x)$$ and
$$y=x / 25$$ ?
Graph "by hand" and see the pattern.

Last edited: Oct 31, 2005