Question

3^(2r)= 9^(2r-1)

Answer 1

Get a common base of 3 by rewriting 9 as 3^2

Answer 2

sorry I don't understand?

Answer 3

so on the right side, it will end up as 3^2(2r-1)

Does that part make sense?

Answer 4

Wait, why is that?

Answer 5

So in order to solve these kinds of problems, both sides need to have the same base. So that means to change either the 3 or the 9

Answer 6

Okay, then what?

Answer 7

Do you understand how 3^2 = 9

Answer 8

Let's get a common base of 9 actually. Look on the left side. Do you see that 3^(2r) is equivalent to 9^r?

Answer 9

Yes, 3^2 is 3x3 =9....?

Answer 10

So what we have is 9^r = 9^(2r-1)

Do you get what I did to get there?

Answer 11

hm.. yeah I thinks so

Answer 12

Okay, just ask me to explain again if you don't get it.

So now that you have a common base, you basically can just ignore the "9^" part and set the exponents equal to each other like so:

r = 2r -1

Answer 13

3^2r = 3^2(2r-1) ..?

Answer 14

Yes that can work as well. Then you would expand the 2 into (2r-1)

Answer 15

You would end up with 2r = 4r - 2 then

Answer 16

Oh distribute , okay

Answer 17

Then you would just isolate for r, and double check by using the original equation

What's your answer?

Answer 18

I got 1?

Answer 19

yeah, and if you try it, r = 1 will work in the original equation

Answer 20

and the original equation would be the one that I put in question?

Answer 21

yeah

Answer 22

when I put in the equation, it would be 81..?

Answer 23

r = 1
3^(2r)= 9^(2r-1)
3^(2(1)) = 9^(2(1)-1)
3^2 = 9^1
9 = 9

Answer 24

Oh, I did one part wrong haha

Answer 25

Do you kind of understand the direction to go with these types of questions? Get the same base, then solve the exponents?

Answer 26

Yes I thinks so, thanks

Answer 27

Okay great, good luck and ask if you need a better explanation