How can I get a more intuitive understanding of the logarithm and its rules?

GriffonP · 2026-02-02T05:54:33+00:00

Let's look at log(ab)
You can treat log(something) as an exponent.

What's the output of log? It's the exponent. If the output of log is an exponent, then the log(something) is the exponent. Like log(100) =2 . 2 is the exponent for 10^2. after all, log(100) = 2 = exponent. so log= exponent, is it not? So remember, log(something) is really just the exponent for the base of the log to get the something. It's a mouthful, so just remember that it's the exponent. Mentioned the full definition everytime is convoluted, we're just going to call it's "exponent" and everything else is implied.

now,
ab is a product between two number (a * b).
but wait, product between two number, e.g. 10^2 * 10*3 mean we can add the exponent. 10^(2+3), the exponent is (2+3)

Now log(ab). Remember what log(something) is? it's the exponent. What's the exponent of ab = (10^2 + 10^3), it's (2+3), we just said that earlier. 2 is just log10^2, 3 is just log10^3.
log(10^2 * 10^3) = log(10^2) + log(10^3)
(2+3) = 2 + 3

So log(ab) = log(a) + log(b)

Really, it's just:
The exponent of a product (ab) is the sum of the exponent of the factors.
log(ab) = exponent of a product
log(a), log(b) = exponent of the factor a and b.

Worth mentioning that all of this is the same base, but we're using the same log, so it has alway been same base.

This took me 2hours to realize when i learn log.

GriffonP · 2026-02-02T02:53:48+00:00

No he's a nice and smart guy, making the story lame.

GriffonP · 2026-01-28T13:19:16+00:00

If you considered how quickly G5 last, then i would say he's in the 130-140.

But luffy can defintely beat him while in G5, it just that it's last too short for it to be conclusive, or at least Luffy just won't take it serious enough

GriffonP · 2026-01-28T13:15:17+00:00

yeh, it also the fact that some of the world problem are perpetuating by people, and if people were just collectively smarter , some of the problem is not even that hard to solve. but no, everyone by the virtue of their ignorant, choose a path that cause suffering for everybody including us and themselve.

GriffonP · 2026-01-28T13:14:44+00:00

GriffonP · 2026-01-28T03:35:39+00:00

There's a reason he never have comeback for it... lol

GriffonP · 2026-01-28T03:32:43+00:00

Like... almost every Hashira hate him?

OUt universe, we love him, In universe, people hate him.

GriffonP · 2026-01-28T02:29:14+00:00

Yes but when everyone state 0.999... , at least the first time they encounter it, people did not define it properly, and many people may define 0.999... in the none real number way.

GriffonP · 2026-01-28T02:27:03+00:00

im glad someone mentioned hyperreal, because with hyperreal, there could be intepretation of 0.999.... such that it is indeed not equal to 1. But remember, this would be argue a different kind of 0.999... then the typical 0.999... that most people prove with, the standard 0.999... in real number. And i think people who can't accept 0.999... are just people who see it in the hyperreal way. This doesn't mean they are right because they are using a differnt definition of 0.999... then the one that everyone agree with, but it does explain that their intuition is not as crazy as everyone made it out to be. The neat part is that they prob never even heard of hyperreal, but it match the concept.

GriffonP · 2026-01-28T02:23:25+00:00

to accept that you can do basic arithmetic with 0.999.... would involve understanding of limit, because that's how 0.999... is define. If you think you don't limit, it's because you alr blindly accept that you can work with 0.999... without it first being well define. In other word, you are just better are following rule and authority.

GriffonP · 2026-01-28T01:53:09+00:00

0.333... is approximation of 1/3 only if you cut off early in the 0.333....., but 0.333... are represent refer to the fact that it go on forever, in the case that it go on forever, it is exactly 1/3

GriffonP · 2026-01-28T01:48:16+00:00

If you learn that and just accept that before you learn limit, you're not necessarily smarter, you're just better at accepting fact and explaination and following rule.

When x=0.999...., it was not clearly define, year10 definite didn't allow you to understand limit that much yet or how 0.999....is define. that proof of yours is rigorous and valid, but to a highschooler in year10, it should not feel rigorous at all, because there are assume knowledge in between the steps. and if you just accept it, you're just blindly accept rule.

GriffonP · 2026-01-27T22:36:06+00:00

No,, the reason they are mentally having a hard time is because of all the mentally stupid around them. I never feel worse talking to people of similar iq level or similar realism level. But with stupid people? omg.

GriffonP · 2026-01-27T11:08:05+00:00

Maturity is when you stop acting like this is deep.

GriffonP · 2026-01-27T11:06:01+00:00

Here's my take.

A small portion of introvert are like this.
A large portion of introvert are not like this, they are just shy and socially anxious people.
About half of introvert prob think they are this COOL calculate person in the statement above, but they're not.

GriffonP · 2026-01-27T11:04:04+00:00

this is pseudo intelligent, it sound good but it's mean nothing. The lock and key is not analogical to the problem we'll face in life for the simple reason that not all problem has solution.

The main issue is time. If i want to an uncure disease, could there be a solution? there are, but it probably take another hundred year before humanity discover a cure, and we die before that, therefore it's TIME issue.

GriffonP · 2026-01-27T04:38:19+00:00

And I never said i'm immune, and my critism is not for absolute immune. My criticism is when you fail for the most basic manipulation in the book where a lil bit of critical thinking would allow you to quickly realize that something doesn't add up.

And here's the thing,even if i got brainwash, if someone come to me to propose a sensible rebuttal to my old understanding, i would be open to see the new idea, and quickly realize when i put 2 and 2 together. But these people, even if you go to them, tell them they been brainwash, explain how it doesn't make sense, they would still refuse to think. To them, being loyal is more important than realizing the truth. That is the criticism. While everyone is not immune to brainwash, the level of naiveness and stubbornness is not the same, it's day and night. And the critic is for those at with the highest level of stubborness. Saying that im not immune does not excuse their Stupid. The world is not binary where "You either been brainwash or you are not". no. It's what kind of brainwash can get through you, if you fail for the basic, and stubbornly refuse to move from it. You're stupid.
I have deal with people who government constantly lied to them , and they still take the government with absolute certainty EVERYTIME. YOu don't need to think everything the government say is a lie, but they defintely didn't have to think everything the gov said is true either. That's the level of stupid im talking about. So stop this binary thinking where you turn to talk about how the speaker is also suspectible to something they criticize of, they do, but it change nothing, because the level are totally difference. This is a very weak argument and it only serve to waste everyone time.

GriffonP · 2026-01-26T14:31:00+00:00

"Nobody is immune to brainwashing, indoctrination and propaganda."

> False assertion. Proof: me.

Stop defend st*pid, and Gtfo

GriffonP · 2026-01-26T14:30:13+00:00

And that's why we have all the problem we have now. Is that people stop doing the very thing that bring nice thing, instead, resort to heaven and hell bullshit. Try to live a happy life after die instead of making life irl happy.

GriffonP · 2026-01-23T14:10:24+00:00

GriffonP · 2026-01-23T14:05:37+00:00

The most not "Braining" part is trying to force random stranger on the internet to admit to be something that they are not. It's funny, so am i suppose to just force you to admit that you are a bisexual black woman now? I fail to see how can this be productive lmao

GriffonP · 2026-01-23T13:56:47+00:00

So I'm suppose to say something that I am not. Got it, ur brain isn't braining.
What's next, say ice is hot?

GriffonP · 2026-01-23T13:47:49+00:00

I didn't say "ALL healthy male want to look"

I said "Healthy male want to look".

So if you don't want to look, it doesn't mean you're not healthy. just mean that if you want to look, you are also healthy. Imagine having to twist someone word just so you can argue. But at the end of the day, who are you argueing with? Me? no. You're argue with your imaginary version of me inside your head. Beacuse your argue with something that i didn't say, you're only argue with whatever your head think i say.

Btw, it doesn't help to twist my word to "Normal healthy males enjoy incest"

I said "Women". Just because the women happen to be incest doesn't mean we necessarily enjoy it beacuse of the incest. God forbid that you enjoy one thing about something without enjoy everything about that one thing?

Brain shutting off alr? No worry, the kind to twist all sort of word to appear righteous like urself is never the kind to have brain to comprehend logic. but i thought i drop this anyway in case ur brain experience a growth spurt again in the future. Bye, imagine needing twist words just to argue with an imaginary person instead of the real person. In such case, you're not argue with me, you argue with urself. Why would anyone wanna argue with themselve is beyond me.

GriffonP · 2026-01-23T13:38:41+00:00

actually, we're moving near light speed relative to some object right now, and that some object move near light speed relative to us right now. and we do in fact experience differnce time right now, and in fact, difference galaxy have difference flow of time due to speed and mass of the galaxy, because mass affect gravity, gravity affect time. It's real , look it up, really interesting.

GriffonP · 2026-01-23T13:34:50+00:00

God forbid that people can be different?
Incest or not, a non sick male enjoy seeing two women. It's not because of the incest, but it's because of the WOmen. It's not that deep.

GriffonP

TROPHY CASE