log e

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

Found between the lower and upper boundaries ... er, I mean decks.

Honestly, given the wordplay I use, I'm surprised I haven't done this one sooner. And I had to go back to find the "ln" guy -- all the way to Comic #454: Log vs. Ln from 2010. If I've used him since, I didn't tag him. (I'm almost certain that I have at least one other time.)

Just in time for the end of the World Series, naturally.

Final note: after being a bit tired Monday and having real-life stuff to deal with yesterday, I decided that my leftover Halloween comic can wait for next year. I left myself a note on my iPad. I should probably back that up.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon. Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.

Come back often for more funny math and geeky comics.

Logged In

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(C)Copyright 2021, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

LoggedIn would be a great numerical social network. Ln for short.

Did you ever notice that whenever no one can log in, there's always someone who knows something and doesn't have a problem.

I also write Fiction! Check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads. Thank you.

Come back often for more funny math and geeky comics.

(x, why?) Mini: Log n

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(C)Copyright 2018, C. Burke.

Because the Math/Pain Scale is logarithmic.




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Algebra 2 Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

15. The loudness of sound is measured in units called decibels (dB).
These units are measured by first assigning an intensity I₀ to a very softsound that is called the threshold sound. The sound to be measured is assigned an intensity, I, and the decibel rating, d, of this sound is found using d = 10 log (I / I₀).
The threshold sound audible to the average person is 1.0 X 10^-12 W/m² (watts per square meter).
Consider the following sound level classifications:

How would a sound with intensity 6.3 X 10^-3 W/m2 be classified?

Moderate	45-69 dB
Loud	70-89 dB
Very Loud	90-109 dB
Defeaning	> 110 dB

(3) very loud

Don't let all the logs and subscripts bother you. At the heart of this question is simple substitution and evaluation. Plug in the values and let the calculator do the rest.
The formula you are given is: d = 10 log (I / I₀).
I₀ = 1.0 X 10^-12, and I = 6.3 X 10^-3
So calculate (using enough parentheses!) the following: 10 log ( (6.3 X 10^-3) / (1.0 X 10^-12) )
You should get 97.99341..., which is between 90 and 109, or "Very Loud".

16. Pedro and Bobby each own an ant farm. Pedro starts with 100 ants and says his farm is growing exponentially at a rate of 15% per month. Bobby starts with 350 ants and says his farm is steadily decreasing by 5 ants per month.
Assuming both boys are accurate in describing the population of their ant farms, after how many months will they both have approximately the same number of ants?

(2) 8

The equation for Pedro's farm is y = 100(1.15)^x. The equation for Bobby's farm is y = 350 - 5x. (Note that Bobby is losing 5 ants, not 5%.)
Graph these on your calculator.
The two lines will intersect at a fraction past 8 months, where both will have a little less than 310 ants.
Use the CALC function (2nd and TRACE) and choose Intersection from the menu. Hit ENTER three times to get the answer.




Continue to the next problems

Algebra 2 Problems of the Day

The following problems were taken from the ALGEBRA II (Common Core) Regents Exam given on Friday, January 27, 2017.
Previous problems can be found here

Part 1

7. The expression

is equivalent to

(2) (see below)

You may do some of these steps in a different order. You might combine several of them.
I'm breaking it down as much as I can so more people can follow along.
Here is my process:

Resolve the division by subtracting the exponents: 2 - (1/3) = 1 2/3 or 5/3.
Next resolve the exponents: to find a power or a power, multiply the exponents, so (5/3)(-1/2) = (-5/6)
A negative exponent indicates the reciprocal: m^(-5/6) = (1 / m^5/6)
A fractional exponent indicates the nth root: see illustration above.

8. What is the inverse of the function y = log ₃ x?

(3) y = 3^x
Logs are the inverse of exponential functions.




Continue to the next problems

Merry Christmas 2014: Yule Logs

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(C)Copyright 2014, C. Burke.

Merry Christmas to all my readers. To those not celebrating, enjoy your day.

It's been a busy time, and truth be told, this was a joke that I wrote down a month before last Christmas and then forgot to do. I planned to do it right this year, but just didn't have time to illustrate it the way I would have liked (and I know my limits). That's not to say that I won't try. So if you come back, maybe not today, maybe not tomorrow, but soon, it'll get updated. If you don't come back, you might regret it, but you'll always have the rough draft.

Roman LOGIC

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(C)Copyright 2014, C. Burke.

LOG 99 = 1996/1000.

Quick bit of research revealed that while the Romans had neither fractions (as we know them) nor decimal points (nor place values, for that matter), they did have expressions for certain parts of whole. In particular, they had words for 1/12, 1/24, 1/48, 1/72, 1/144, and 1/288. The names for the latter three are very similar according to one source, unfortunately, searching on the word for 1/72 (scriptulum), I was informed by several other sites that that word actually meant 1/288.

Whichever word it was, the Romans had a system for "one off", by putting a prefix like "de" in the front, it would mean one 1/72 off the whole, which would mean 71/72. In this case, whichever that word was, one plus that fraction would be the closest approximation to log₁₀ 99.

Well, it would be if they'd had logarithms.

Sure! If they actually had them, I'd love for you to post a link in the comment section! Thank you for asking!

Happy New Years Eve 2013

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(C)Copyright 2012, C. Burke. All rights reserved.

40 log sin(x)

This might explain it better.
Happy New Year 2013

Log vs. Ln

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(C)Copyright 2010, C. Burke. All rights reserved.


I came close to having a "natural E" eighth note bounce in on the right side, but then all the "see sharp" and "be flat" jokes came to mind.

I always hated logarithms, but at least I could understand what base 10 was. How do you have a base where you don't even know what the number is? Why not 2? Why not pi? Oh, yes, because this irrational number was "natural"!