mersenneforum.org  

Go Back   mersenneforum.org > New To GIMPS? Start Here! > Homework Help

Reply
 
Thread Tools
Old 2010-07-08, 15:54   #1
Unregistered
 

2×5×419 Posts
Default An algebraic quandry

Hello all,

I am a tutor with a student who was a professor with a habit of assigning very challenging derivative problems for extra credit. The last two I have helped this student with are well over 40-50 steps to actually solve. On the current problem, which I will not type out because it would take forever to get the notation and parentheses and exponents correct, I have hit a bit of a wall on simplifying. Note: I can still find the solution but it would be easier if I can implement a different strategy. My question is this:

I know logarithms of like bases can be combined via VERY basic log rules -aka ---

log(x) + log(x) = log(x^2) = 2 log(x) My student knows this as well. However, my question is this: Is there any relationship between more complicated expressions such as:

log(x)*log(x) + log(x) which does NOT equal 2*(log(x))^2

If so, can this be extended to even more complicated expressions such as:

log(A)*log(B) + log(C) where A, B, and C are all linear or exponential expressions involving the independent variable x.

Note- I do not care how ugly the expression gets- I rather like ugly expressions. However, my student's knowledge is limited to Calc 2, mine is limited to ODE

Thanks!
  Reply With Quote
Old 2010-07-08, 16:53   #2
Orgasmic Troll
Cranksta Rap Ayatollah
 
Orgasmic Troll's Avatar
 
Jul 2003

641 Posts
Default

Quote:
Originally Posted by Unregistered View Post
Hello all,

I am a tutor with a student who was a professor with a habit of assigning very challenging derivative problems for extra credit. The last two I have helped this student with are well over 40-50 steps to actually solve. On the current problem, which I will not type out because it would take forever to get the notation and parentheses and exponents correct, I have hit a bit of a wall on simplifying. Note: I can still find the solution but it would be easier if I can implement a different strategy. My question is this:

I know logarithms of like bases can be combined via VERY basic log rules -aka ---

log(x) + log(x) = log(x^2) = 2 log(x) My student knows this as well. However, my question is this: Is there any relationship between more complicated expressions such as:

log(x)*log(x) + log(x) which does NOT equal 2*(log(x))^2

If so, can this be extended to even more complicated expressions such as:

log(A)*log(B) + log(C) where A, B, and C are all linear or exponential expressions involving the independent variable x.

Note- I do not care how ugly the expression gets- I rather like ugly expressions. However, my student's knowledge is limited to Calc 2, mine is limited to ODE

Thanks!
How can an ugly expression be simple?

and if any of A, B, or C are simply exponential expressions, what do you get when you take the log of an exponential expression?
Orgasmic Troll is offline   Reply With Quote
Old 2010-07-08, 16:57   #3
Unregistered
 

204548 Posts
Default

Exponential expressions including x... For example:

log(x^2-3)*log(x^3 -1) + log(2x+5)
  Reply With Quote
Old 2010-07-08, 17:09   #4
Orgasmic Troll
Cranksta Rap Ayatollah
 
Orgasmic Troll's Avatar
 
Jul 2003

28116 Posts
Default

Those are not exponential expressions. Those are polynomials. I fear for your students.
Orgasmic Troll is offline   Reply With Quote
Old 2010-07-08, 23:57   #5
Primeinator
 
Primeinator's Avatar
 
"Kyle"
Feb 2005
Somewhere near M50..sshh!

2·3·149 Posts
Default

I had a similar question myself. The only rule I know of is log (a) + log (b) = log (ab) or log (a/b) for subtraction.

Orgasmic Troll, I think he/she means logarithmic arguments containing exponential terms -ex binomials or other forms of polynomials.

Last fiddled with by Primeinator on 2010-07-08 at 23:59
Primeinator is offline   Reply With Quote
Old 2010-07-09, 12:18   #6
Mini-Geek
Account Deleted
 
Mini-Geek's Avatar
 
"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts
Default

Quote:
Originally Posted by Unregistered View Post
log(x)*log(x) + log(x) which does NOT equal 2*(log(x))^2

If so, can this be extended to even more complicated expressions such as:

log(A)*log(B) + log(C) where A, B, and C are all linear or exponential expressions involving the independent variable x.

Note- I do not care how ugly the expression gets- I rather like ugly expressions. However, my student's knowledge is limited to Calc 2, mine is limited to ODE

Thanks!
Keeping in mind that x*log(y)=log(y^x) and log(x)+log(y)=log(xy):
\log A *\log B + \log C =
\log{(B^{\log A})} + \log C =
\log(C*B^{\log A})
Which of course is the same as \log(C*A^{\log(B)}) since multiplication is commutative (log(A)*log(B)=log(A^log(B))).
if x=A=B=C, (meaning the original equation was \log x *\log x + \log x) then that expression is equal to:
\log(x*x^{\log x}) =
\log(x^{\log(x)+1})
Hey, you said you didn't care if it gets ugly.

Last fiddled with by Mini-Geek on 2010-07-09 at 12:38
Mini-Geek is offline   Reply With Quote
Old 2010-07-09, 13:42   #7
R.D. Silverman
 
R.D. Silverman's Avatar
 
Nov 2003

22×5×373 Posts
Default

Quote:
Originally Posted by Orgasmic Troll View Post
Those are not exponential expressions. Those are polynomials. I fear for your students.
As do I. He/she seems incompetent.
R.D. Silverman is offline   Reply With Quote
Old 2010-12-05, 11:26   #8
lorgix
 
lorgix's Avatar
 
Sep 2010
Scandinavia

3×5×41 Posts
Default

People come here for help. They obviously know that they could be more competent.
lorgix is offline   Reply With Quote
Old 2010-12-05, 11:45   #9
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

25·52·13 Posts
Default

Quote:
Originally Posted by R.D. Silverman View Post
As do I. He/she seems incompetent.
Quote:
Originally Posted by lorgix View Post
People come here for help. They obviously know that they could be more competent.
[pontification]
When faced with these two statements, I must confess that I prefer the second. As I see it, everyone is incompetent in the sense that no-one knows everything and and can do everything in a particular field. To that extent, Bob's statement is correct but (largely) vacuous.

On the premise that everyone can improve their level of competence if they wish to do so, lorgix's statement appears to me to be much more positive.

I am concerned, as is Bob, that all too often some people are attempting to work at a level above the required degree of competence. Such people, if they are willing to take action, should be encouraged to learn and those capable of teaching them should attempt to do so. Ignorance is a curable condition.
[/pontification]

Paul
xilman is online now   Reply With Quote
Old 2010-12-05, 11:55   #10
cmd
 
cmd's Avatar
 
"(^r'Β°:.:)^n;e'e"
Nov 2008
;t:.:;^

33×37 Posts
Default

every ignorant can learn what it ignores,
then every jurisdiction should learn to smile
its jurisdiction
cmd is offline   Reply With Quote
Old 2010-12-05, 23:05   #11
davar55
 
davar55's Avatar
 
May 2004
New York City

102068 Posts
Default

Ignorance is curable
Tho some think unendurable
Before one claims that he knows more
He oughta know just what's in store
davar55 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Algebraic factors in sieve files pepi37 Conjectures 'R Us 95 2017-07-04 13:37
Introduction to Algebraic and Abelian Functions bearnol Miscellaneous Math 2 2015-12-30 05:32
Algebraic factor issues base 24 michaf Conjectures 'R Us 18 2008-05-21 10:08
Algebraic factors henryzz ElevenSmooth 13 2007-12-18 09:12
NFS algebraic square root questions jasonp Factoring 17 2007-01-10 07:37

All times are UTC. The time now is 18:14.

Sat Dec 5 18:14:02 UTC 2020 up 2 days, 14:25, 0 users, load averages: 2.67, 2.57, 2.44

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.