Math Is Fun Forum

Oh, I've got a clue why I cannot reach it under normal circumstances.

Because-

It has got a word of "Revolution"

Darn my Government!!

PS: I am in China.

I Love PROXY!

Without you I cannot Surf!

I Love PROXY!

Without you I cannot Play!!

Simple.

First, logs. A Log means how many times it can take you to multiply a certain number to another.

i.e.

2*2*2=8 Thus the log for 8 at the base 2 is 3

Further, fraction log is defined as this

the log for 2 at the base 8 is 1/3, Since the backward is 3. 3 times vs 1/3, pretty fair.
also we can say the log for 4 at the base 8 is 2/3, think why.

And, negative log can be defined.

the log for 1/8 at the base 2 is -3, since the log for 1/8 at the base the reciprocal of 2 is 3.

Altogether you can find that for a given base>1, a log for some number larger than it should be larger than 1
and a log for some number smaller than it but as well larger than 1 is smaller than 1 as well as positive. The log for 1 at  any vaild base ,a positive number, is 0. At last, a log for some number smaller than 1 at a base larger than 1 is negative.

ln function means to calculate a log for x at a certain base.
Try to calculate ln0.5 and see if the result corresponds with a base larger than 1.
Try to calculate ln2.71828 and ln2.71829 and think what the certain base is. Can you tell a interval where it lies in?

Uh oh, see why the whole question is so important in maths?

Actually the orginal integral is unintegrable, I mean cannot be expressed by simple combinations of functions , +-*/sincostanlog.

A logic book may help you.

Impresive indeed...

Yes, Linear!
-1(x)
So e[sup]-y[/sup]|'[sub]y[/sub]=e[sup]-y[/sup](-1)

Uh, got it. I think the misunderstanding came from the either one conclusion-I thought you began to doubt whether reals are dense if they are not equal.

Yes, amazing. But it need around 100 aditional rules, which are related to the machine itself rather than being universal maths rules, to fully manupulate, whereas a slide rule needs less than 10.

I will show you many other maths magic a slide rule can perform. Wait...

G) Narcissism-> leaders with a high self-esteem may think he is the center of the universe and without his "ingenius" management, the people he leads may fall into a mass. This is supported by philosopher Pope, that a person with a single value system may stick to "design" the society. And he suggested it is the utmost cause of totalitarism in the East in 20th century.

Unintegrable as far as my software can tell.