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View Poll Results: What is log(10)
2.3025 9 16.67%
1 43 79.63%
42 2 3.70%
Voters: 54. You may not vote on this poll

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  #61  
Old 05-01-2018, 05:03 PM
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Originally Posted by Vorian Atreides View Post
Give a description of what the natural log is without referencing e . . .
The indefinite integral of 1/x
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  #62  
Old 05-01-2018, 05:04 PM
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It's like asking me to explain base 10 log without using 10.
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  #63  
Old 05-01-2018, 05:10 PM
BernieSanders2016 BernieSanders2016 is offline
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Originally Posted by Vorian Atreides View Post
Give a description of what the natural log is without referencing e . . .
It would be impossible, or if it was possible it would have no meaningful value as a description, but why do we need to avoid referencing e?
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  #64  
Old 05-01-2018, 06:04 PM
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log(10) = i.
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  #65  
Old 05-01-2018, 06:23 PM
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How do you pronounce "ln"? Is it like "lawn"?
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  #66  
Old 05-01-2018, 06:37 PM
BernieSanders2016 BernieSanders2016 is offline
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How do you pronounce "ln"? Is it like "lawn"?
I always pronounce it like "Ellen" in my head.
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  #67  
Old 05-01-2018, 09:49 PM
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How do you pronounce "ln"? Is it like "lawn"?
len
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  #68  
Old 05-01-2018, 10:11 PM
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Vorian Atreides Vorian Atreides is offline
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Quote:
Originally Posted by DanielSong39 View Post
It's like asking me to explain base 10 log without using 10.
While true, there is a pedagogical difference to understanding the log function using something already familiar to the student. (See below.)

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Originally Posted by BernieSanders2016 View Post
It would be impossible, or if it was possible it would have no meaningful value as a description, but why do we need to avoid referencing e?
Consider that most students familiar with exponents will catch on to the following very easily (and naturally):

log10(x) = y <==> 10^y = x

And most will also see the connections to other bases and quickly extrapolate the general nature of the log function:

log2(x) = y <==> 2^y = x



However, e isn't a number that students will find a meaningful value for in and of itself. Continuous compounding might be the closest thing one might get to something "natural" that students would start to grasp the value of this number (much like a "natural" connection of pi to two familiar quantities of a circle). But outside of that, it takes quite some time to get students to connect to the usefulness of ln(x) for many problems until they do get to calculus.

But the earlier concepts I showed will help the student make the better connection to the power of e and ln(x) for addressing most problems in science and finance.
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  #69  
Old 05-01-2018, 10:12 PM
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Quote:
Originally Posted by Polevault1 View Post
How do you pronounce "ln"? Is it like "lawn"?
"log".
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  #70  
Old 05-01-2018, 10:14 PM
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https://www.youtube.com/watch?v=sULa9Lc4pck
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