Algebraic structure : Group

  • Thread starter naoufelabs
  • Start date
  • #1
17
0
Please I have a problem with natural log for group set as follow:


a*b=eln(a)*ln(b)

1- Show that the group law * is associative and commutative
2- Show that the group law * accept an element e (Identity element)

Thank you !
 
Last edited:

Answers and Replies

  • #2
lavinia
Science Advisor
Gold Member
3,264
646
Please I have a problem with natural log for group set as follow:


a*b=eln(a)*ln(b)

1- Show that the group law * is associative and commutative
2- Show that the group law * accept an element e (Identity element)

Thank you !

what are you stuck on?
 
  • #3
17
0
Sorry, I mean to achieve to result that a*b = b*a, and a*e=a.
But I'm stuck on.
Thanks
 
  • #4
360
0
You answered lavinia's question...by not answering it. As a start, use the definition you wrote in your first post to write out what a*b, b*a, and a*e are.
 
  • #5
Deveno
Science Advisor
908
6
is elna*lnb the same as, or different than elnb*lna?

show us your work so far
 
  • #6
17
0
I tested with Maple e^ln(a)*ln(b), then the result is a^ln(b).
so I tested with 2 different numbers, example:
3^ln(2) = 2^ln(3) ==> Gives the same result.
So I found that the e^ln(a)*ln(b) is commutative.
 
  • #7
22,129
3,298
I tested with Maple e^ln(a)*ln(b), then the result is a^ln(b).
so I tested with 2 different numbers, example:
3^ln(2) = 2^ln(3) ==> Gives the same result.
So I found that the e^ln(a)*ln(b) is commutative.

No, you have tested it with two arbitrary numbers. You have to test it for all numbers!!!!
Just checking it with two numbers does not suffice at all!!

You must show that a*b=b*a. Write out the definition of * and show us what it means.
 
  • #8
Deveno
Science Advisor
908
6
I tested with Maple e^ln(a)*ln(b), then the result is a^ln(b).
so I tested with 2 different numbers, example:
3^ln(2) = 2^ln(3) ==> Gives the same result.
So I found that the e^ln(a)*ln(b) is commutative.

get a piece of paper, and use your brain. Maple won't solve this one for you.
 
  • #10
17
0
Thanks for all
 

Related Threads on Algebraic structure : Group

  • Last Post
Replies
7
Views
5K
Replies
5
Views
843
Replies
3
Views
4K
Replies
3
Views
2K
Replies
9
Views
273
Replies
1
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
9
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
2K
Top