User:Guy vandegrift/sandbox

I presume this is my sandbox where I can do anything that is not illegal or grossly inappropriate.

Template:Hidden begin content to be hidden placed here Template:Hidden end

Joke fails

I assume this is like a user page on wiki. My first task is to adjust to your wiki; it looks simpler (more primitive) than Wikipedia. For example, my joke fails because your templates are different:

{{cot|What is physics? (click for answer)}} {{cot|Physics is}} {{cot|what physicists do}} {{cot|late at night.}} {{cob}} {{cob}} {{cob}} {{cob}}

Template:Begin-foldable What is foldable? Template:End-foldable

That's because this is not wikipedia. There is no intention for it ever to be wikipedia. We have pirated templates from them on occasion, but rarely, because they tend not to be very good. --prime mover (talk) 06:07, 19 February 2015 (UTC)

Playing with equations

<math>E=mc^2</math>

So you indent differently. Not a bad change. Lets try mathcal:

<math>\mathcal{ABCDEFG}</math>

Experimenting with the editing tools at the bottom of the edit page

\(\ds first \ \ \)

\(\ds second\)

\(third\)

\(\ds fourth\)

\(\ds fifth\)

sixth

\(\quad\) seventh

I find this change of base proof easier to remember

https://en.wikiversity.org/w/index.php?title=Speak_Math_Now!/Week_9:_Six_rules_of_Exponents/Logarithms&oldid=2362681#Change_of_base

Randomly pick one of the bases, and solve for the other base:

<math>b=B^{N/n}</math>

Now we take a logarithm of each side:

If <math>B</math> is the base: <math>\log_B(b)=\log_B(B^{N/n})=\frac N n \log_B (B)=\frac N n = \frac{\log_B(x)}{\log_b(x)},</math> which leads to:

<math>\log_b(x)=\frac{\log_B(x)}{\log_B(b)}</math>

If <math>b</math> is the base: <math>\log_b(b)=1=\log_b(B^{N/n})= \frac N n \log_b (B)=\frac{\log_B(x)}{\log_b(x)}\log_b (B), </math> which leads to:

<math>\log_B(x)=\frac {\log_b(x) }{\log_b(B)} </math>