# Another &quot;impossible&quot; A Level question

Discussion in 'Mathematics' started by DM, Jan 17, 2012.

1. ### DMNew commenter

Well not exactly impossible but ambiguous. However I don't think this one is worthy of another media frenzy.
Today's OCR MEI Core 2 paper asks:
log_a (a^3)^6 =
I think most of you will agree the expected answer is 18. However a significant number of people have given 729 as the answer as they believe the logarithm takes precedence over the final index.
log (10^3)^6 =
or ln (e^3)^6 =
Oh dear.

2. ### bobboots

tbh I agree with your students.

3. ### DMNew commenter

Not my students but you would think OCR MEI would have checked everything with a fine-toothed comb after the previous exams season fiasco.

4. ### KarvolOccasional commenter

Why would the logarithm take precedence? Unless I am misreading the question ( quite possible as I have just returned from a school function involving copious amounts of alcoholic substances), there is a world of difference between
log_a (a^3)^6 and (log_a (a^3))^6.

5. ### DMNew commenter

As I said, if you have the necessary coordination, prod the buttons of your calculator.
MathCAD also agrees with the log first rule.
Wolfram doesn't.
Edit: Who would believe that adults are banned from using the word prod?

6. ### bobboots

I guess this is a good example of why we like cos^2(x) rather than cos(x)^2
Maybe it should have been log_a^6( a^3)

7. ### DMNew commenter

Indeed. And we also say ln^2 x for the same reason so an unambiguous notation does already exist.
Edit: You edited and now my remark looks redundant!

8. ### mathsteacher1953

My Casio gives an answer of 18.
I must admit that given all the possible questions to test their understanding of logs, it seems odd to create one like this. Ours sat the paper today but I haven't had my copy yet. Students seemed happy enough.

9. ### DMNew commenter

My Casio (fx83) gives 729.

10. ### davidmuOccasional commenter

Why is anyone considering using a calculator? The answer is instant by inspection of 18.

11. ### PiranhaStar commenter

Modern Casios insert brackets on functions such as Log, so the user decides the order calculations are done in. I would have interpreted it as intended.
This all begs the question about why a question should be set which can be done on a calculator with little understanding of the underlying concepts. I assume some sort of working will be expected to get the marks. I would also think that candidates misinterpreting the question will get something.

12. ### scraggy55New commenter

Agreed. If a student needs a calculator for this question, then they don't understand the concept of logarithms; and the concept is being tested here, not the (correct) use of a calculator.

13. ### Polecat

DM: 'My Casio (fx83) gives 729'
My fx83MS gives 18, but my fx83ES gives 729.
Interesting..

14. ### DMNew commenter

That really is interesting. You would expect consistency in the same model.

15. ### DMNew commenter

I don't think it is as simple as some of you appear to think. I'm not suggesting that candidates reached for a calculator at all. I am suggesting that there is a debate to be had about the "correct" order of operations here. I fully expect both answers to be accepted in the end.

16. ### Polecat

Polecat: 'My fx83MS gives 18, but my fx83ES gives 729.
Interesting.'.
...and my fx-85MS gives 1.800000000 x 10^1.

17. ### DMNew commenter

Is your fx-85MS in Sci mode?
And is this the calculator equivalent of philately?

18. ### Polecat

'Is your fx-85MS in Sci mode?'
Yes, just to illustrate the many faces of calculator output.
'And is this the calculator equivalent of philately?'
My album is rather chunky.

19. ### florapost

how did you get tes to allow that word? long since banned from many a toxic argument in 'opinion' wrt n ireland.

20. ### drnfp

Totally agree with davidmu. That's why we have exams. Any pupil who thinks it's 729 by inspection or calculator will get a lower grade, as they should.