anonymous
  • anonymous
On the same axis graph y=cosx and y=(1/2)^x and state four points where cosx=(1/2)^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
I graphed them both using software I can see the points. How do I go about solving for the points algebraically?
anonymous
  • anonymous
How to solve for: \[ \cos x = \left(\frac 1 2\right)^x \]?

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anonymous
  • anonymous
Hey wio
anonymous
  • anonymous
Yes i was thinking of taking log ofboth sides
anonymous
  • anonymous
Started drawing a blank when i tried to doit
anonymous
  • anonymous
There isn't any nice way of doing it.
anonymous
  • anonymous
lol
anonymous
  • anonymous
I mean im guessing im supposed to solve for it right?
anonymous
  • anonymous
I posted the screenshot from my textbook as well
anonymous
  • anonymous
You can use Newton's root finding method. It's not nice because it doesn't always work.
anonymous
  • anonymous
The chapter I'm doing goes through composition of functions if that helps
anonymous
  • anonymous
This is the very last question for grade 12 advanced functions
anonymous
  • anonymous
lol
anonymous
  • anonymous
Just looking at it you can see that \(x=0\).
anonymous
  • anonymous
Ya noticed that too, but I dunno if thats sufficient
anonymous
  • anonymous
There may be some other intersections as well.
anonymous
  • anonymous
I never heard of this newton root umentioned so i doubt i have to use it
anonymous
  • anonymous
It's Calculus.
anonymous
  • anonymous
Using the natural logarithm here won't help you.
anonymous
  • anonymous
I was thinking of using the normal logarithm on both sides
anonymous
  • anonymous
\[ \ln(\cos(x)) = x\ln(1/2) \]Does not get you anywhere.
anonymous
  • anonymous
to get rid of the exponent
anonymous
  • anonymous
Yeah, unfortunately I don't think there is any algebraic way to do it.
anonymous
  • anonymous
\[ \ln(\cos(x)) = x\ln(1/2) \]Does not get you anywhere.
anonymous
  • anonymous
Ok thx
anonymous
  • anonymous
Anyone else wanna take a stab at it?
anonymous
  • anonymous
Photo of question at the top as well
anonymous
  • anonymous
@SithsAndGiggles
anonymous
  • anonymous
I can think of one solution of the top of my head. Not sure about the others, or how to find them for that matter. \(x=0\) is one.

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