# 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