Mrs. RickJay is having a rough time with her homework because we can’t get the damned calculator - a Casio fx-270w - to work right.
She’s learning logarithms. Our understanding is that if
x^y=b
then
logx(b)=y
Specifically we’re working on problem 3^x=229. Use the log to find x. I absolutely cannot get the calculator to do it, not for love or money. Now, I’ve found an online calculator that does it very easily; the answer is about 4.94, which I coould have guessed because 3^5=243. But I simply cannot get this scientific calculator to use the LOG button to produce the answer 4.94. If I type
3 then LOG then 229 , I get 7.08, which is wrong.
If I type
229 then LOG then 3, I get 109.something, which is wrong.
If I type
LOG 3 (229) I get 109something again.
If I type
LOG 229 (3) I get 7.08 again.
If I type
LOG (3)229 I get a syntax error.
All I’m getting are multiples of the natural logs, not the answer X. Help! Are we misunderstanding how to solve the problem?? Or are we typing it in wrong?
I didn’t think there was a shorter way…that’s how I’ve always done logs on my calculator…you have to take the log of both sides first, then remember that log x^y = y*logx, and then just divide normally…
3^x = 229
log(3^x) = log229
but log(3^x) = xlog(3)
therefore
xlog3 = log229
x = log229/log3 = 4.946
I suppose it could be punched into a calculator in one try, but it would require more brackets than I care to think about!
RickJay, ultrafilter’s right. Unless you want to solve this by taylor series expansion or something equally ugly, you’d want to type:
229
log
/
3
log
Some calculators have strict left to right processing and so you may require typing the log first.
Basically, the formula is log(229)/log(3) using the same log base in both cases (doesn’t matter what log base it is, if you have multiple log keys, just as long as you use the same each time).
In this case, b is the destination base (3), x is the value to take the log of (229), and a is the base of the log function you do have (in this case the natural log, e).
Interestingly (to me, at least), this is one operation I still find easier to do with my trusty K&E Log Log Decitrig (all you old dopers can now give us your nostalgic stories about hating your sliderules.)
I’d love to find one of those classroom model sliderules they used to hang over the blackboard: aluminum with black lettering, about 5 feet long and a foot tall. Anyone under 40 probably wouldn’t have any idea what is was.
Oh, but I do. The high school I graduated from back in 1985 had one. I was the only one who knew how to use it. Of course, that’s because I had my Dad’s old cheapo plastic one to play with as a kid. He used to use it when calculating explosive charges (mixtures and amounts of diesel and nitrate fertilizer) that he used in his limestone quarry. When it became brittle and broke, I latched onto a couple of K+Es at an auction. One is plastic but it has lots more funtionality (Log-Log and trig.) The other is much simpler, but ir is made of teak wood with what looks like ivory (although it is probably just plastic.) I also have a K+E Circular that I bought when I was in TechSchool in the Air Force. I didn’t use it in class, but it sure came in handy for calculating currency conversions when I got stationed in Germany later that year.
I also own a couple of Sharp EL5500s, a TI99-4A, a programmable TI with LED display whose model number escapes me at the moment, a Linux powered PDA with scientific calculator, and more little four bangers than you can shake a stick at. I once built a frequency counter out of and old desktop calculator that had a Nixie tube style display. It only counted up to about three kilohertz, but it was enough for the stuff I was fiddling with at the time.
Is it too obvious that I like calculating machines?
When I first learned about this, I thought of it as the long way too. So I wrote a program on my graphing calculator that would take logarithms in any base! It really really wasn’t worth it; I had wasted much more time writing the program than I ever would save using it. I deleted the program after using it once.
Well, it works to divide the base 10 logs, obviously, but I have to admit I’m surprised there’s no function on a scientific calculator where you can just type in LOG, then the base, then the product, and get the answer. Strange, because you’d think it would mirror the way it’s generally written on paper.
Thanks for the link, sailor! I too was born in '67, but learned to use the slipstick out of sheer interest. Knowing how and why the thing works is a marvelous eye-opener to the world of matematics.
You just need a more expensive calculator. I have one with an set of alphanumeric keys, so I can do base 60 arithmetic. The nice thing about it is I can type in “Secret of life?” and it only takes 6 seconds to give me the answer.
Well, Rick, I agree, it’d be helpful to do logs in any base, but since it only takes a few extra keypresses to do logs in any base on a calculator anyway, possibly calculator designers (at least cheap ones) don’t think it’s worth it.
How about 1.42524 to the base 7.88423?
log(1.42524)/log(7.88423)
where log is the base-anything log (say base 10).
Works ducky.
0.17160458227366649282749431464654
So 7.88423 ^ 0.17160458227366649282749431464654 is 1.42524.
