Bug: HP Prime can't do Log's

[davimle]

Wow! I think I definitely came to the right place instead of continuing to waste time with HP Support. I am happy to see that there is such an active, enthusiastic and vibrant community for the Prime. I'm not sure if it came across correctly my original post, so I wanted to re-emphasize here, both my wife and I love our HP 28S calculators and I even run an RPN calculator on my iPhone because I couldn't stand being without one all the time! If it wasn't for our firm love of HP calculators, I wouldn't have sent our daughter down this path. However, I have to remind people she is only 15 and a Sophomore in a U.S. High School (glad to see the diverse participation here!) dominated by TI's calculators and their teaching curriculum. My daughter is not tech adverse, but she doesn't have a fundamental love of digging into things "behind the scenes", so I would say she is a "typical" user rather than an "expert" user. So thank you so much to everyone who has replied so far, I have definitely learned some new things (which is good!).

@Cyrille (et al) I actually had confirmed that CAS would get the right answer to LOG(A,B), however I had asked my daughter to only use CAS mode for "fun" and to stay away from it day to day because it is not allowed and disabled on tests. Both in class and for SAT, AP, etc. Again, I love the CAS mode and it is extremely powerful, just not as appropriate for someone at the beginning of learning math. (I should have included this in the OP.)

Further, thank you for pointing out that the machine may be doing LN(A)/LN(B) behind the scenes. I hadn't thought too hard about how LOG(A,B) was implemented, but this makes sense and the results do confirm this seems to be what is happening. And I agree with @CR Haeger about a "teachable moment" and maybe we can talk about numerical methods! (Hadn't thought it would come up so soon, but may be a good opportunity.) Though I do agree with @Dieter that if this is what is happening behind the scenes, then additional precision should be used to hide this from the user.

@Han thank you for pointing out proot() she did not find that, and now I have downloaded the full User Guide for her. Looks like just what she wanted, so thank you, I had not found this via Google search. (Probably because I was searching on "quadratic".) Knowing what to type, or where to find functions will certainly help. I will check tonight (she has the calculator at school now) if it also works in non-CAS modes. I will look more at the Help and Catlg methods and point her to these. Thx.

@TW, she was using the Solver app before, but it would only return one root and would require some guessing on a "seed" to return the other root. Again, as you know as a "teaching" calculator, the others put in a more "easy to use" function.

@cclinus thank you for pointing out the "Rounded to 10" number format. I think this may make sense in that 11 was a bit "odd" anyways. This might be a useful work-around and alternative to Scientific or Engineering formats, given they also round.

@retoa & @Cyrille I think you have the "winner" here! Sorry that I did not know there was a logb(A,B) function. My daughter only showed me LOG(A,B) and it seemed to be working other than the few problematic cases. Also thank you for pointing out the template menu, she will like using that because she was complaining that the Sharp has better algebraic entry of log(B)A. I also confirmed this returns correct answer in Home mode last night same as @jebem.

In fact, after downloading the full User Guide, I can not find the LOG(A,B) function documented. So looks like there is more than one way to do a log of arbitrary base. (Not sure how she figured it out, but she found LOG(A,B).) I'll have her stick to the template and logb.

@carey you made me laugh out loud (in a good way!) I am reminded of the popular Engineer vs. Mathematician jokes. Being an engineer, you know how I side, but it's always refreshing to learn something new.

@TW thank you for the detailed explanation. As an engineer I understand the complexities of numerical approximations and limited precision, however as a "teaching" calculator in addition to a scientific and engineering calculator you have to play some of the same tricks as your competitors. I'm glad the problem made it through to the right technical team at HP. The responses I got from the Support representatives were not reassuring.

Thankfully, I think the consensus here is using 15 digit precision for the LOG(A,B) calculation solves the problem. Are we to correctly assume that is what was already being done for logb(A,B)? Given that LOG(A,B) seems to be undocumented, I am fine with sticking with logb(A,B). Might want to make sure the Support team knows to point people there as a solution rather than trying to say that the successive error returns the right answer. Any reason for both logb() and LOG() each with different implementation?

Finally, nothing but love and appreciation to everyone who took their time to point. I really am heartened by the fun responses I read here. I feel much better about the Prime knowing what is happening behind the scenes. Now I just have to hope the ACT comes to their senses before my daughter has to take it to avoid having to buy any TI calculator!