Solving a System of Equations Without a Calculator

[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!

 

[Tide]

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

 

[PhysicsinCalifornia]

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!

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$$(-\infty, \infty)$$

 

[dragon513]

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$$(-\infty, \infty)$$

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?

 

[ivybond]

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?

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.