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Is this working right/Random questions

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cara.mel:
I have lots of trouble with Log (not so much with Exponential, but that is hard too), I can visualise them fine but I don't understand any of the rules for it.

I am sorry if the latex is shite (it looks all squished up, ie the lines are particularly friendly towards each other)






Making the substitution now because my friend said so:



**is this right?

∴ (does Latex have therefore?)




Then, as
*why does e^ln x = x
∴ 
Can this be simplified still?



Why does
Why does (I don't care if that last expression is actually sinh x, I am stupid and don't know which one has + and which one has - in it, I think I got it right =/)

Mao:
for "squished up", you usually put extra line spacing when using fractions, etc

, that is correct.

that expression for y does not appear like it can be simplified any further.

is euler's formula. the proof for it can be found here: http://en.wikipedia.org/wiki/Euler's_formula#Using_calculus

the definition of the hyperbolic functions are the odd and even parts of the natural exponent, that's just the way it is defined. and you are right, that is the expression for cosh.

cara.mel:
Thank you mao

How can I learn rules for Exponential and Log.

Why are some things 'impossible' to solve algebraically?

Mao:














thats all i think...

cara.mel:
why are they like that

why does e^ln gfkjfdsgkj = gfkjfdsgkj

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