Functions- inverse of logarithm

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KingRich
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Hi,

This is a fairly simple question.

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I found the inverse to be
y=in x ÷ in 2

The text book shows y= In₂ x

According to desmos both show that they are correct.

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Can someone confirm my understanding of this please
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mqb2766
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(Original post by KingRich)
Hi,

This is a fairly simple question.

Name:  DE7B271B-BE98-4105-979A-F6AB629FEF82.jpeg
Views: 15
Size:  40.9 KB


I found the inverse to be
y=in x ÷ in 2

The text book shows y= In₂ x

According to desmos both show that they are correct.

Name:  A0E1FFFD-FF74-4CAC-83DD-05F03E92D40C.jpeg
Views: 12
Size:  91.9 KB

Can someone confirm my understanding of this please
Thats correct. The inverse of 2^x is log_2(x) which, using the change of base formula, is also equal to ln(x)/ln(2). Or more generally
log_2(x) = log_b(x)/log_b(2)
for some base b.
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KingRich
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(Original post by mqb2766)
Thats correct. The inverse of 2^x is log_2(x) which, using the change of base formula, is also equal to ln(x)/ln(2). Or more generally
log_2(x) = log_b(x)/log_b(2)
for some base b.
So, in a test for example. Either would be correct?
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mqb2766
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(Original post by KingRich)
So, in a test for example. Either would be correct?
Both should be ok, but log_2(x) would be the obvious one because its the inverse "by defintion" and you usually give the simplest answer.

Note in the OP you said that the book said y=ln(x) is the inverse. ln() is usually the natural log, so log_e(), so as per above the answer would be ln(x)/ln(2). Your desmos defintions were fine so I didn't pick it up in the previous reply.
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KingRich
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(Original post by mqb2766)
Both should be ok, but log_2(x) would be the obvious one because its the inverse "by defintion" and you usually give the simplest answer.

Note in the OP you said that the book said y=ln(x) is the inverse. ln() is usually the natural log, so log_e(), so as per above the answer would be ln(x)/ln(2). Your desmos defintions were fine so I didn't pick it up in the previous reply.
Okay. Great my first exam is 7th June lol

I have over estimated myself by miles, mainly because I got really Ill!! But overall I’m confident in what I’ve learnt so far, so here’s hoping I don’t fail too much lol.
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mqb2766
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(Original post by KingRich)
Okay. Great my first exam is 7th June lol

I have over estimated myself by miles, mainly because I got really Ill!! But overall I’m confident in what I’ve learnt so far, so here’s hoping I don’t fail too much lol.
Good luck and make sure you hit the past exam papers before then.
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KingRich
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(Original post by mqb2766)
Good luck and make sure you hit the past exam papers before then.
Mmm, I was planning to print them all off up to 2019 as far as I could find but it’s a lot of pages lol!!!!

So, I’m having to use the desktop, which won’t reflect the same set up but it should help me in terms of the layout of the questions etc

And thank you
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mqb2766
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(Original post by KingRich)
Mmm, I was planning to print them all off up to 2019 as far as I could find but it’s a lot of pages lol!!!!

So, I’m having to use the desktop, which won’t reflect the same set up but it should help me in terms of the layout of the questions etc

And thank you
Its worth it (at least from the time the syllabus changed), and if you need some extra exercises, have a look at edexcel as well (you're doing aqa?) as they're not that different.
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KingRich
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(Original post by mqb2766)
Its worth it (at least from the time the syllabus changed), and if you need some extra exercises, have a look at edexcel as well (you're doing aqa?) as they're not that different.
Mmm, that’s correct. As far as I have learnt the only real difference is the data bank that they use for statistics and the layout of their exams with paper 1 and 2 being pure only and 3 being a combination of mechanics and statistics, which is a setup that I think I’d prefer lol.
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mqb2766
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(Original post by KingRich)
Mmm, that’s correct. As far as I have learnt the only real difference is the data bank that they use for statistics and the layout of their exams with paper 1 and 2 being pure only and 3 being a combination of mechanics and statistics, which is a setup that I think I’d prefer lol.
Its just a throwaway comment. Use the recent AQA papers first, then if you need some other stuff, something like edexcel is a reasonable resource. Also pmt has the 2021 assessment material
https://www.physicsandmathstutor.com...maths-a-level/
which is a reasonable chunk of questions for each topic.
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KingRich
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(Original post by mqb2766)
Its just a throwaway comment. Use the recent AQA papers first, then if you need some other stuff, something like edexcel is a reasonable resource. Also pmt has the 2021 assessment material
https://www.physicsandmathstutor.com...maths-a-level/
which is a reasonable chunk of questions for each topic.
Thank you
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