good kid, maad city - a small-town kid's A-level journey

This needs updating.

Yes!! Awfully quiet couple of days

I have a pretty big update for tonight

Um, didn't feel like making a thread for this, but why is



I understand the later that ln(e^x) = x

$x * ln(e) = x * 1 = x$

(I hope it's fine to ask here)

Um, didn't feel like making a thread for this, but why is



I understand the later that ln(e^x) = x

$x * ln(e) = x * 1 = x$

(I hope it's fine to ask here)

$e^x$ and $\ln x$ are inverse operations. So composing them together gets you $x$.

i.e: $f(x) \circ f^{-1}(x) = x$.

Here we have $f(x) = e^x \Rightarrow f^{-1}(x) = \ln x$ or $f(x) = \ln x \Rightarrow f^{-1}(x) = e^x$.

It's the same reason why $\sqrt{x^2} =x$, because $\sqrt{x}$ and $x^2$ are inverse functions.

It's the same reason why $\sqrt{x^2} =x$, because $\sqrt{x}$ and $x^2$ are inverse functions.

$e^x$ and $\ln x$ are inverse operations. So composing them together gets you $x$.

i.e: $f(x) \circ f^{-1}(x) = x$.

Here we have $f(x) = e^x \Rightarrow f^{-1}(x) = \ln x$ or $f(x) = \ln x \Rightarrow f^{-1}(x) = e^x$.

It's the same reason why $\sqrt{x^2} =x$, because $\sqrt{x}$ and $x^2$ are inverse functions.

Your explanations of stuff like this are just brilliant

However, this only applies on a certain domain, right?

...

Your explanations of stuff like this are just brilliant

If I was on the maths forum I'd have put in a bracket to specify:

(blah blah, yes, this is only true if we restrict the domain of $x \mapsto x^2$ to be an injective function i.e, we need $x\geq 0$).

But I figured I needn't on here.

BTW: Big update?

I was only teasing you lad I like how you can change gears from Maths nerd Zacken to bantz Zacken so easily.




I'll post it first thing tomorrow morning! I did a lot of conic sections tonight and I feel like I don't suck AS bad anymore...

When are you doing your mocks? I tried the S3 paper and the first 4 questions were very nice, but I couldn't proceed past it because I'd didn't cover contingency tables or gof for continuous distributions. You'll love a few of those questions though!

His post yesterday or the day before killed me.

"HA GOT YOU"

Zacken420 XD that entire thread was on drugs...

I honestly had never seen that part of him come alive before

He also admitted that he has a vagina, let's not forget He's definitely been hitting some good stuff after results day. 🌚

He also admitted that he has a vagina, let's not forget

say what?

He implied that he menstruates

Oh, that explains the moodiness every month then