# Foo - Is this logarithm equation properly condensed?

Bikeforums.net is a forum about nothing but bikes. Our community can help you find information about hard-to-find and localized information like bicycle tours, specialties like where in your area to have your recumbent bike serviced, or what are the best bicycle tires and seats for the activities you use your bike for.

phantomcow2
11-04-08, 07:19 PM
ln(e+1) - ln(e^2) + ln(e) =

ln(e*1) = ln(e)

ln(e)/ln(e^2)(e) Divide because of the subtraction.

but ln(e) = 1, and ln e^2 * e = e^3. Lne^3 = 3.

pgoat
11-04-08, 07:30 PM
if you foo egg heads are gonna go at it tonight don't just stand there - pls count us some votes or something!

Minesbroken
11-04-08, 07:47 PM
no...?

ehidle
11-04-08, 07:51 PM
I am working on another problem right now that is far more pressing. I am trying to take a pile of about 150 red poker chips and turn them into more than 270, all using only the will of my mind...

It's proving to be difficult.

:p

Gogga Logga
11-04-08, 07:53 PM
I wrote an amusing solution to Phantom's question in the margin of Bike Forums. But now I'm feeling...argh...[thud]

pgoat
11-04-08, 07:54 PM
well, so long as you are using your time productively

seriously, you guys with your physics and organic chem threads are making me feel as stupid as I really am.

I am thinking about taking some night classes in math/science. I'm one of those humanities people, so it'll be like teaching Gary Coleman to slam dunk. But life needs a challenge, huh?

apricissimus
11-04-08, 07:57 PM
I'm having a hard time understanding what you're doing...

ln(e + 1) - ln(e^2) + ln(e) =
ln((e + 1)/e^2) + ln(e) =
ln(((e + 1)/e^2)*e) =
ln((e + 1)/e)=
ln(e + 1) - ln(e) =
ln(e + 1) - 1

Or more simply:

ln(e + 1) - ln(e^2) + ln(e) =
ln(e + 1) - 2*ln(e) + ln(e) =
ln(e + 1) - 2*1 + 1=
ln(e + 1) - 1

RubenX
11-04-08, 08:03 PM
and there's why this electronic engineer wannabe settled for computer analyst nighshifter...

MrCrassic
11-04-08, 08:14 PM
http://www.sitmo.com/gg/latex/latex2png.2.php?z=150&eq=%5Cln(e%2B1)-%5Cln(e%5E2)%2B%5Cln(e)%20%5Crightarrow%20%5Cln(e%2B1)-%7B2%5Ccdot%5Cln(e)%7D%2B%5Cln(e)%20%5Crightarrow%20%5Cln(e%2B1)-1

Remember that:

http://www.sitmo.com/gg/latex/latex2png.2.php?z=150&eq=%5Cln(e)=1

and

http://www.sitmo.com/gg/latex/latex2png.2.php?z=150&eq=%5Cln(e^a)=a%5Ccdot%5Cln(e)

MrCrassic
11-04-08, 08:21 PM
ln(e+1) - ln(e^2) + ln(e) =

ln(e*1) = ln(e)

ln(e)/ln(e^2)(e) Divide because of the subtraction.

but ln(e) = 1, and ln e^2 * e = e^3. Lne^3 = 3.

Attempting to go by your logic, I think where you may have gone wrong was assuming that this was an equation, i.e. you assumed that there was something that it related to. The problem was asking you to reduce the expression, so there was nothing to move that ln(e) statement to.

pgoat
11-04-08, 08:21 PM
oh yeah, I remember now:rolleyes:

SegFault
11-05-08, 08:59 AM
Stay away from condensed expressions, dude. I only use freshly-squeezed expressions.

MrCrassic
11-05-08, 10:52 AM
Make sure it doesn't have concentraet.

apricissimus
11-05-08, 11:14 AM
No, you need to concentrate in order to solve these problems.

UnsafeAlpine
11-05-08, 11:21 AM
http://www.sitmo.com/gg/latex/latex2png.2.php?z=150&eq=%5Cln%28e%2B1%29-%5Cln%28e%5E2%29%2B%5Cln%28e%29%20%5Crightarrow%20%5Cln%28e%2B1%29-%7B2%5Ccdot%5Cln%28e%29%7D%2B%5Cln%28e%29%20%5Crightarrow%20%5Cln%28e%2B1%29-1

Remember that:

http://www.sitmo.com/gg/latex/latex2png.2.php?z=150&eq=%5Cln%28e%29=1

and

http://www.sitmo.com/gg/latex/latex2png.2.php?z=150&eq=%5Cln%28e%5Ea%29=a%5Ccdot%5Cln%28e%29

ln e^a = a

pgoat
11-05-08, 11:21 AM
E = sightsee MC

MrCrassic
11-05-08, 11:24 AM
ln e^a = a

That's true, but I was demonstrating the principle.

UnsafeAlpine
11-05-08, 11:26 AM
That's true, but I was demonstrating the principle.

yeah, I got it, I just like the shorthand version better. Much less messy... ;)

MrCrassic
11-05-08, 11:31 AM
:)

KingTermite
11-05-08, 12:07 PM
Thank John Napier (http://en.wikipedia.org/wiki/John_napier) you have them as a tool in the first place.

phantomcow2
11-05-08, 03:07 PM

pgoat
11-05-08, 03:14 PM
you're welcome

MrCrassic
11-05-08, 03:18 PM
:)

apricissimus
11-05-08, 03:24 PM
We need more of these in schools:

http://www.screensite.org/courses/Jbutler/T389/SlideRule.jpg

And fewer of these:

http://images.amazon.com/images/P/B00001N2QU.01._SCLZZZZZZZ_.gif

SegFault
11-05-08, 04:22 PM
We need more of these in schools:

<snipped image>

And fewer of these:

<snipped image>

Agreed.

When I was in high school, my physics teacher had a supply of slide rules plus instruction booklets that were handed out to any student who forgot their calculators (this was when all the cool kids had TI-86s) on exam days. It then became a bit of a machismo contest to see who could get the best marks using the slide rules. By the end of the course, we realized that the graphing calculators aren't nearly as essential as we once thought.

MrCrassic
11-05-08, 04:46 PM
I can't see the images right now, but if you guys are talking about calculators, then I agree wholeheartedly.

I don't own a graphing calculator. I've had to borrow one a few times on test to make quick computations (i.e. QUICK! What's ln(2.965)/sqrt(9.5478)??). When I need a calculator, I use the one on my phone (with the phone fcn off). It's so much better to learn mental math tricks.

An acquaintance of mine was studying with a TI-92 VOYAGER on his desk. If you haven't seen the thing, it's like a mini-computer JUST for math. If I ever needed that kind of computational prowess, that assignment is getting done on my PC. And GNU/Octave or MATLAB is a HELL of a lot more powerful than any graphing calculator.

You guys are making me miss doing horribly in math. Stop it. :p

apricissimus
11-05-08, 10:29 PM
I can't see the images right now, but if you guys are talking about calculators, then I agree wholeheartedly.

I don't own a graphing calculator. I've had to borrow one a few times on test to make quick computations (i.e. QUICK! What's ln(2.965)/sqrt(9.5478)??). When I need a calculator, I use the one on my phone (with the phone fcn off). It's so much better to learn mental math tricks.

An acquaintance of mine was studying with a TI-92 VOYAGER on his desk. If you haven't seen the thing, it's like a mini-computer JUST for math. If I ever needed that kind of computational prowess, that assignment is getting done on my PC. And GNU/Octave or MATLAB is a HELL of a lot more powerful than any graphing calculator.

You guys are making me miss doing horribly in math. Stop it. :p

I got the TI-92 when it first came out, which is basically the same as the Voyage. I also have the TI-89, which is the same as the TI-92, but without the qwerty keyboard.

At work I use the new TI-Nspire. It's really creeping toward the "computer" paradigm rather than the calculator paradigm. Texas Instruments doesn't even call it a calculator. It's a "handheld", with analogous software that you can run on your computer. The computer software does everything that the handheld does, but is prettier and easier to use. With the growing ubiquity of computers and laptops, I kinda wonder why anyone would use the handheld.

The TI-Nspire CAS (Computer Algebra System) version has all the symbolic manipulation capabilities of the TI-89 and TI-92, but unlike the 89 and 92, it's aimed at high school students. So rather than learn to factor polynomials, for example, students can get the Nspire to do it for them. And people in math education circles are very excited about this. They think it will free up students to learn higher level concepts without being bogged down in details. I think it'll just lead them to not learn how to do basic math. It kinda depresses me.

It's as if you'd expect students to learn about music theory without playing an instrument. It makes no sense to me.

</tangent>

jschen
11-06-08, 01:27 PM
We need more of these in schools:

<slide rule>

And fewer of these:

<graphing calculator>

How about neither, and actually build good back of the envelope estimation skills? My first graduate level chemistry course was in physical organic chemistry. Lots of calculations involved, and no calculators (or slide rules) allowed on the exam. There were logarithms and exponents (as one might expect with thermodynamics and kinetics problems) and numerical answers were expected.

apricissimus
11-06-08, 01:45 PM
How about neither, and actually build good back of the envelope estimation skills? My first graduate level chemistry course was in physical organic chemistry. Lots of calculations involved, and no calculators (or slide rules) allowed on the exam. There were logarithms and exponents (as one might expect with thermodynamics and kinetics problems) and numerical answers were expected.

I do agree with you, but I like the slide rule because you actually have to do something, unlike a calculator which just spits the answer out at you. I think you actually get a feel for how logarithms work with a slide rule.

But yes, mental arithmetic and estimation is sorely lacking among... well, everyone really. Which is not to say that calculators and other aides don't also have their place. I just worry that we are complacent about letting them become a crutch that we can't do without.

MrCrassic
11-06-08, 02:15 PM
How about neither, and actually build good back of the envelope estimation skills? My first graduate level chemistry course was in physical organic chemistry. Lots of calculations involved, and no calculators (or slide rules) allowed on the exam. There were logarithms and exponents (as one might expect with thermodynamics and kinetics problems) and numerical answers were expected.

How long did it take you to compute those logs and exp's in your head?

If I had a large block of time during a test (like a final), then I can make approximations like that. However, using log rules takes a few seconds, if the numbers are easy. A calculator can compute that much more quickly.

I don't like using them, but they are handy when they are handy.

jschen
11-06-08, 04:36 PM
How long did it take you to compute those logs and exp's in your head?

It became (and 10 years later, still is) more or less second nature. The idea, according to my prof, was that one should always be able to sanity check someone else's presentation when at a conference/seminar, and one doesn't have a calculator when at the talk, nor does one have time to do paper calculations. So one does a good ballpark estimation just to make sure things seem reasonable. The key is to work in base 10, since humans think in base 10 and not in base 2.718.... Then for back of the envelope purposes...

log 2 ~ 0.3
log 3 ~ 0.5
log 4 ~ 0.6
log 5 ~ 0.7
log 6 ~ 0.8
log 7 ~ 0.85
log 8 ~ 0.9
log 9 ~ 0.95

These are more than close enough to the real values to be useful for a single sig fig answer. And heck... by using some simple log manipulations (for example, for log 72, I'd treat that as log 9*8, or log 9 + log 8), I could get pretty close for two sig figs on the fly back when I was in the class. (Not anymore, though... out of practice.) Of course, to do that in a useful manner, one needs to know the above values to two sig figs, which nowadays I find kind of pointless in my line of work. So one sig fig it is, other than log 7 and log 9. [edit: Checking the values, only log 3 and log 6 need to be modified... log 3 ~ 0.48, log 6 ~ 0.78. The other values are correct to two sig figs.]

gapowermike
11-06-08, 07:01 PM
A real calculator...

http://www.hpmuseum.org/11c.jpg