Question

I'm not sure how to work this problem out.
Solve open parentheses square root of 6 close parentheses to the 8 x power = 216x−3
Please help.

Answer 1

\[(\sqrt{6})^8=216x - 3?\]

Answer 2

Yes

Answer 3

Pls verify correctness of my previous entry.

Answer 4

Now, simplify the radical:\[(\sqrt{6})^8=?\]

Answer 5

Note that this is th

Answer 6

this is the same as \[((\sqrt{6})^2)^4=?\]

Answer 7

The equation you did the first time looks like the one I have. I'm just not sure on how to solve it.

Answer 8

What's the square of the square root of 6?

Answer 9

2.4?

Answer 10

Oh @mathmale I noticed in your equation you drew you didn't put 8x in the power. You just put 8.

Answer 11

That's an indication that you need to use parentheses to show that the '8' and the 'x' go together. Please type in the original problem again, using parentheses so that there is no possibility of misinterpretation.

Answer 12

Okay, sorry I'm new at this.
6^(8x)=216^(x-3)

Answer 13

@mathmale is this better?

Answer 14

That's a totally different problem, which emphasizes why you need to use parentheses whenever there's any possibility of doubt as to what you mean.\[6^{8x}=216^{(x-3)}\]

Answer 15

Is 216 an integer power of 6? If so, write 6^x=216. Show your work, please.

Answer 16

I'm not sure about what your asking. :(

Answer 17

6 raised to what power equals 216?

Answer 18

All I know is that 6 and 216 are the base and I need them to be the same. Once they are the same I take those away and just focus on the powers, but the radical sign is throwing me off. I am so confused! Ugh! I forgot the radical sign in my equation! I am so so so sorry! There should be a radical with the 6.

Answer 19

Please, make the effort to answer my question about 6 and 216. First I asked you whether 216 is an integer power of 6. It is. Next I asked you "6 raised to what power equals 216?"

Try raising 6 to the 1st, 2nd, 3rd, 4th and 5th powers. That might help establish the necessary pattern in your mind.

Answer 20

Okay would it be 6^3?

Answer 21

Yes.

Now re-write my most recent equation as is, except, replace "216" with "(6^3)".

Answer 22

So it would be 6^(8x)=6^(3)(x-3) with x-3 still in the power?

Answer 23

Yes. Now you have the same base on both sides of your equation. What is it?
Equate the power on the left side to the power on the right side.

Answer 24

I think now I just have to use the powers, but I need to distribute the 3. Is that correct?

Answer 25

Yes. I'd rather that you plunge ahead and try things like this. You don't need my approval.

Answer 26

Left side: expo is 8x.
Right side: expo is ..... ?

Answer 27

Now we have 8x=3x-9?

Answer 28

Yes. Again, don't wait for my approval. Go ahead / plunge ahead and find x; we will verify whether or not your result is correct or not.

Answer 29

Your result: x = ??

Answer 30

-3?

Answer 31

If 8x=3x-9, how would x come out equal to -3? Have I made any math errors? or have you?

Answer 32

I think I did. Let me try again.

Answer 33

Would I do this:
8x=3x-9
8x-3x = 3x-3x - 9
5x=-9
5x/5 = -9/5
x=-1.8?

Answer 34

Here's where you'll need to check your own work.
You began with 8x = 3x - 9.
If you substitute x =-1.8, is the resulting equation true or not?

Answer 35

It is true!

Answer 36

So, what is your conclusion?

Answer 37

x=-1.8
8x=3x-9
8(-1.8)=3(-1.8)-9
-14.4=-14.4

Answer 38

Indeed. But I was askin you, "What does the fact that this check-up equation is true tell you about your solution to the original problem?"

Answer 39

I'm not sure what you mean by that. :(

Answer 40

I think I've got it now. Thank you!

Answer 41

You've checked your result and found that your "check equation" was true. That means y our solution to the original problem is most likely correct.
Please review what I said about using parentheses for enhanced clarity.
Good work.
See you again.