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# C2 graph/logs question watch

1. Hey guys,

I'm a bit stuck with part 3 of this question. Mainly with rearranging the equation to get a half somewhere. I worked out the answer to the first half using a different method but I can't quite get the method they're using to get the answer to the y coordinate of p

x = -0.32

Attachment 508687508689
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2. (Original post by Saywhatyoumean)
Hey guys,

I'm a bit stuck with part 3 of this question, rearranging the equations to get a half in the equation. I worked out the answer to the first half of using a different method but I can't quite get the method they're using to get the answer to the y coordinate of p

x = -0.32

Attachment 508687508689

please post your workings
3. (Original post by TeeEm)
please post your workings
Okay well I put the two equations equal to each other straight away and took logs of both sides:

(1/3)^x = 2(3^x)

Xlog1/3 = log 2(3^x)

xlog(1/3) = log2 + xlog3

Xlog1/3 - xlog3 = log2

X(log1/3 - log3) = log2

X= log2/log1/9

X= -0.32

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4. (Original post by Saywhatyoumean)
...
If you've found , then you can just plug that value right back any of your two equations or and they'll both give you the y-coordinate out.

It's kind of like how, if you have a line and then they intersect at , which is the x-coordinate of the intersection, but also the y-coordinate is given by plugging that into or .
5. (Original post by Saywhatyoumean)
Okay well I put the two equations equal to each other straight away and took logs of both sides:

(1/3)^x = 2(3^x)

Xlog1/3 = log 2(3^x)

xlog(1/3) = log2 + xlog3

Xlog1/3 - xlog3 = log2

X(log1/3 - log3) = log2

X= log2/log1/9

X= -0.32

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(Original post by Zacken)
If you've found , then you can just plug that value right back any of your two equations or and they'll both give you the y-coordinate out.

It's kind of like how, if you have a line and then they intersect at , which is the x-coordinate of the intersection, but also the y-coordinate is given by plugging that into or .
Zacken has already started helping you
all the best
6. (Original post by Zacken)
If you've found , then you can just plug that value right back any of your two equations or and they'll both give you the y-coordinate out.

It's kind of like how, if you have a line and then they intersect at , which is the x-coordinate of the intersection, but also the y-coordinate is given by plugging that into or .
Thanks for this, I knew that but x was a very long decimal and subbing it in to get y didn't give me a nice answer of root 2, it was a few decimal places out so I didn't think I'd get the marks for doing that here? I'm not sure though

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7. (null)

Again thanks, I got roughly something like that but what happens to the 1^x in that - wouldn't it be 1^x/2 = 3^x ?

I feel like that's a stupid question

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8. (Original post by TeeEm)
Zacken has already started helping you
all the best
Thanks lol

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9. (Original post by Saywhatyoumean)
Thanks for this, I knew that but x was a very long decimal and subbing it in to get y didn't give me a nice answer of root 2, it was a few decimal places out so I didn't think I'd get the marks for doing that here? I'm not sure though

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You're not meant to use the decimal answer, you should use the exact value instead:

So you know that , then:

How can you work out exactly? Use the fact that

Does that help?
10. (Original post by Zacken)
You're not meant to use the decimal answer, you should use the exact value instead:

So you know that , then:

How can you work out exactly? Use the fact that

Does that help?
Ohh yes it does! Still would never have thought to do that in exam - but what about with this method:

So if (1/3)^x = (1^x/3^x) = 2(3^x)

1^x = 2 x (3^2x)

1^x / 2 = 3^2x ?

What happens to the 1^x ?

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11. (Original post by Saywhatyoumean)
Ohh yes it does! Still would never have thought to do that in exam - but what about with this method:

So if (1/3)^x = (1^x/3^x) = 2(3^x)

1^x = 2 x (3^2x)

1^x / 2 = 3^2x ?

What happens to the 1^x ?

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1^x = 1 for all x.
12. Anyone know which paper this is from?
13. (Original post by Zacken)
1^x = 1 for all x.
omg of course how did I not see that😂😂thanks!

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14. (Original post by anonwinner)
Anyone know which paper this is from?
it's one of the OCR Solomon papers, H I think

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15. (Original post by Saywhatyoumean)
it's one of the OCR Solomon papers, H I think

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thanks

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