Question

Find the three points of intersection with the equation -x^2 = -2^x, please show step by step.

Answer 1

x=2

Answer 2

if the base is the same number then you just have to solve the exponents. which would show that 2=x

Answer 3

do you kind of get what im saying?

Answer 4

Yes. But I know that there are two other solutions, right?

Answer 5

I am actually trying to find the three points of intersection.

Answer 6

oh

Answer 7

@myininaya @ganeshie8 Anyone?

Answer 8

so you actually mean \[x^2=2^x ? \]

Answer 9

Yea

Answer 10

Acctually wait it's -x^2 = -2^x

Answer 11

But unless that's another form for it

Answer 12

so you mean it is \[-1 \cdot x^2 =-1 \cdot 2^x \]

Answer 13

I just want to make sure you are actually looking at \[2^x=x^2\]

Answer 14

ok

Answer 15

My textbook just showed it as how i stated so i just left it like that

Answer 16

but can you show me step by step? I know that there are at least 3 intersections

Answer 17

well if it is the equation you said it is then we could rewrite it as \[2^x=x^2\]

Answer 18

ok

Answer 19

so are you taking calculus and using an approximation method or are you using a more of a guess method and plugging sort of method

Answer 20

there is no straight forward algebra way to solve this

Answer 21

Im taking calc so I guess it's approximation method

Answer 22

what kind of approximation method?

Answer 23

No wait, actually, can we do it the guess method way?

Answer 24

i can only guess two solutions
i can't think of a third

Answer 25

which two solutions are u thinkin?

Answer 26

that one guy said 2^2=2^2

what other integer would give us the same thing on both sides of x^2=2^x?

Answer 27

i will give you a hint
another solution is \[2^{something }\]

Answer 28

4

Answer 29

yep

Answer 30

4^2=2^4
16=16

Answer 31

i'm not sure if i can help you anymore though

Answer 32

Ok, i just plugged this equation into wolfram and the third intersection is a -0.766, but idk how they got that

Answer 33

i dont think it can solved algebraically more like a calculator approximation
so i'll just list that so my teacher will know

Answer 34

thank u

Answer 35

you can use newton's method