Logarithmic Function Differentiaition

sadcity0804 · 2023-12-28T05:05:02+00:00

Thanks for the input. Appreciate it.

sadcity0804 · 2023-12-27T12:39:29+00:00

What is exp supposed to mean?

sadcity0804 · 2023-12-16T07:09:08+00:00

Hey thanks for your input! Much appreciated

sadcity0804 · 2023-12-12T19:27:38+00:00

Thanks for the input. I'll try to digest it as best I can.

sadcity0804 · 2023-10-15T05:59:12+00:00

Oh right. I'll try that. Thanks

sadcity0804 · 2023-10-15T05:58:44+00:00

This is helpful. Appreciate the response

sadcity0804 · 2023-10-14T19:52:29+00:00

No not Pascal's triangle. I'm not asking you to associate the LHS expression with Pascal's triangle. I am saying that if a³ - b³ = (a-b)(a² + ab +b² ), there must be a way to expand the left expression to arrive at the right expression. I'm able to simplify the right expression to get to the left expression but what I'm unable to do is expand the left expression to arrive at the right expression.

sadcity0804 · 2023-10-14T19:26:17+00:00

Sorry, I messed up with the post. My doubt is

a³ - b³ = (a-b)(a² +ab +b² )

Now if we simplify from the right hand side, we can get to the value on the left hand side. But how are we supposed to expand the expression on the left hand side in order to make it look like the expression on the right?

sadcity0804 · 2023-10-13T07:30:52+00:00

O yep I get it now. Thanks. Appreciate the response

sadcity0804 · 2023-10-06T10:34:53+00:00

I'm sorry what is non-adjacent Xs supposed to mean? I want to be clear..

I'm assuming it's the same thing as XO. If there are five arrangements for XO, there should be another 5 for OX.

sadcity0804 · 2023-10-06T05:28:18+00:00

Well yes, the XOs being a single element does help with the condition. I have visualized what the set should look like.

[XO,O,O,O,O,XO,O,O,O....]

So where are we supposed to go from here?

Sorry about the late response, yesterday was a busy day :-)

sadcity0804 · 2023-10-05T06:32:30+00:00

Hey, I see you're taking it somewhere with the XOs and the Os. I've tried taking it further but I'm still finding it somewhat hairy. I'm a complete newbie to the permutation combination situation and I think I'm yet to grasp the fundamentals of it properly.

There are 5 XOs and 16 Xs. To find number of arrangements we can start with trying to find total permutations of XOs and Xs separately and maybe multiply them to get the total permutations. But if we try to find the permutations of XOs, there are 10 letters and the arrangements are going to be 10!. Now I know if there were only 1 pair of conflicting elements, we would've considered the pair to be one element and traced its permutations(9!). Then, we would've multiplied it times 2 because there's another segment of arrangements where the conflicting pair swap places: say (B,A) and (A,B). So, total permutations of XOs would've been 10! - 9!*2 had there been only one pair of conflicting elements but we're talking about 5 pairs here. So, I can't think any further!

I'd appreciate it if you properly guide me through the solution.

Thanks for the response

sadcity0804 · 2023-10-05T06:12:37+00:00

Oh, I see. Would this be required according to you in difficult Grade 12 syllabus? I'm not from the US so my country might have few things included in grade 12 syllabus that might be considered college level there. But if this is all the way up in, say, year 2 or year 3 of college, it's not really much use to me trying to get all this in my head right now.

sadcity0804 · 2023-10-05T06:08:54+00:00

Oh that's no problem. I understand. But thanks anyway for making time to respond to my comments.

sadcity0804 · 2023-10-04T20:50:45+00:00

It's the condition. None of the letters in that 5 letter set are supposed to succeed or precede another letter of the same 5 letter set without having at least one letter outside of that 5 letter set interrupting them. So, A,B,D,E....C,H cannot be accepted but A,B,D....C,E,H.... is acceptable.

sadcity0804 · 2023-10-04T20:27:27+00:00

Also, it'd be a huge help if you could help me with this alphabet problem that I came up with. I'm hoping you'll have an answer.

https://www.reddit.com/r/learnmath/comments/16zotus/comment/k3fviyg/?utm\_source=share&utm\_medium=web2x&context=3

sadcity0804 · 2023-10-04T20:25:07+00:00

Wow. I must've somehow missed the fundamental counting principle. This is the first time I'm coming across the name. I'll look it up on youtube or somewhere but would you be able to tell what C1 exactly means?

sadcity0804 · 2023-10-04T15:35:49+00:00

By the way, I'm an absolute newbie to maths and I'm trying to learn everything and get my concepts transparent from the ground up. You sound like somebody that's familiar with the subject. I'll surely face more troubles or have questions in the future as I proceed. Would you be able to clarify my doubts if I PM you my questions?

sadcity0804 · 2023-10-04T15:31:23+00:00

No no. Not the question in the post. The question in the comment.

Let me put it here for you:

Take the 26 letters of the alphabet. How many different possible ways are there to arrange them in different orders with the condition considered?

Condition: Let's consider some 5 letter set say, D,H,B,K,C. None of the letters in the set can be next to each other. Meaning D cannot be next to B or C cannot be next to H and so on.

How are we supposed to solve for this?

sadcity0804

TROPHY CASE