Question

See the equation.

Answer 1

\[3^{x}(3^{x+2})\]

Answer 2

=9

Answer 3

Are you solving for X?

Answer 4

Yes :)

Answer 5

Let's see, give me a sec. I think there will be some logarithms in here

Answer 6

Alright, thanks!

Answer 7

Ok. so distributing you can see we would get \[3^{2x+2}=9\]

We can rewrite 9 as \[3^{2}\]

Answer 8

So we would get \[3^{2x+2}=3^{2}\]

then take the log base 3 of both sides and

then \[2x+2=2\]

Answer 9

Then you can solve for x

Answer 10

But don't you have to multiply the 3's?

Answer 11

Oh wait. You multiply its squared to the x?

Answer 12

You would take the logbase 3 of both sides \[\log_{3} ( 3^{2x+2}) = \log_{3} (3^{2})\]

Answer 13

leaving you with only exponents

You could also maybe see it straight up as well. \[3^{2x+2} = 9 \]

Answer 14

what is 9 it is 3 squared, so you would know x must be 0

Answer 15

I don't see how you get rid of the other three without having to make it into a \[3 ^{x^{2}}\]

Answer 16

Have you ever worked with logarithms? Maybe I am taking the wrong approach ^_^;

Answer 17

I guess you know this much we can write your equation like \[3^{2x+2}= 3^{2}\]

Answer 18

No, I'm in geometry hehe. My teacher didn't even tell us that this topic was logarithms!

Answer 19

Haha. Well in this problem we don't necessarily need them to solve. We see we can write the expression as \[3^{2x+2}= 3^{2}\] each side with the same base so It is clear the exponents on the left must add up to what we have on the right, in our case 2, so x must be 0!

Answer 20

\[3^{x}(3^{x+2)}=9\]

Answer 21

Where do you get the 2x?

Answer 22

Rules of exponents :

if we are multiplying like terms we add exponents
\[X \times X = X^{2} or X^{1+1}= X^{2}\]

Answer 23

Okay

Answer 24

so what I did in your example is \[3^{x+2+x}\]

Answer 25

combine like terms to get \[3^{2x+2}\]

Answer 26

I actually meant one, and put two by accident! sorry >_< So it's \[3^{2x+1}=9\]

Answer 27

so x=4?

Answer 28

X = 1/2 in this one

Answer 29

Look at it like this \[3^(2x+1) = 3^{2}\]

Answer 30

Whoops, should be: \[3^{2x+1} = 3^{2}\]

Answer 31

We know \[3^{2} = 9\]

Answer 32

Oh, I see my mistake! I forgot to make the 9 into 3^2

Answer 33

Thank you ^_^!

Answer 34

Yeah it is a bit more clear that way :D No problem anytime

Answer 35

I have more questions about this, and I was hoping if you could answer some of them? I have 9 I don't know out of 30

Answer 36

Ok sure!

Answer 37

Thank you so much!

Answer 38

Not a problem. Hopefully I can be of some help.

Answer 39

My first fan! :D lol