Question

On the same axis graph y=cosx and y=(1/2)^x and state four points where cosx=(1/2)^x

Answer 1

I graphed them both using software I can see the points. How do I go about solving for the points algebraically?

Answer 2

How to solve for: \[
\cos x = \left(\frac 1 2\right)^x
\]?

Answer 3

Hey wio

Answer 4

Yes i was thinking of taking log ofboth sides

Answer 5

Started drawing a blank when i tried to doit

Answer 6

There isn't any nice way of doing it.

Answer 7

lol

Answer 8

I mean im guessing im supposed to solve for it right?

Answer 9

I posted the screenshot from my textbook as well

Answer 10

You can use Newton's root finding method. It's not nice because it doesn't always work.

Answer 11

The chapter I'm doing goes through composition of functions if that helps

Answer 12

This is the very last question for grade 12 advanced functions

Answer 13

lol

Answer 14

Just looking at it you can see that \(x=0\).

Answer 15

Ya noticed that too, but I dunno if thats sufficient

Answer 16

There may be some other intersections as well.

Answer 17

I never heard of this newton root umentioned so i doubt i have to use it

Answer 18

It's Calculus.

Answer 19

Using the natural logarithm here won't help you.

Answer 20

I was thinking of using the normal logarithm on both sides

Answer 21

\[
\ln(\cos(x)) = x\ln(1/2)
\]Does not get you anywhere.

Answer 22

to get rid of the exponent

Answer 23

Yeah, unfortunately I don't think there is any algebraic way to do it.

Answer 24

\[
\ln(\cos(x)) = x\ln(1/2)
\]Does not get you anywhere.

Answer 25

Ok thx

Answer 26

Anyone else wanna take a stab at it?

Answer 27

Photo of question at the top as well

Answer 28

@SithsAndGiggles

Answer 29

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.