# What is logarithm how that table is made?

1. Nov 1, 2008

### arjunkr

I am not a physics or math student ,but i am interested in physics i want to understand the nature So i started studying physics my main source is internet .So i need help from people like U .

1.what is limits how and where it is used ?

2.what is logarithm how that table is made?

3.what is pie(22/7) what it is why its value equal to 3.1428?

2. Nov 1, 2008

### HallsofIvy

1 "Limits" are a way of dealing with "instantaneous" changes. For example, using the "algebra" formula "speed= "change in distance/change in time", we MUST have some time change so that we are not dividing by 0. Acceleration, defined as "change in speed/change in time" has that same problem, twice. But by Newton's law of gravity, the acceleration due to gravity depends on distance, which can be measured at a given instant. In order for that to make sense, we must be able to define "speed at a given instant" as well as "acceleration at a given instance". Limits allow us to do that.

2. A logarithm is the "reverse" of the "power" function. For example, 1000= 103 so log10(1000)= 3. I know, because I can multiply, that 34= 81. Because I have seen that, I could solve the equation "3x= 81": x= 4, of course. But what if the problem were "3x= 43"? I know that 33= 27 and that 34= 81. Since 43 is between 27 and 81, I know x is between 3 and 4, but where between? If we define "log3(x)" to be the reverse of 3x, then the answer is "log3(43)". Fortunately, we don't need to have a lot of different tables with different bases because logarithm in any base can be converted to any other base- such as base 10, "common logarthms". Also fortunately, people have devoted a lot of time to solving such problems and making up tables of logarithm solutions- and now we have calculators that give the values very easily.

3. "$\pi$, a Greek letter commonly written "pi" (NOT "pie" which is a desert!) is defined as the ratio of the circumference of a circle to its diameter (ratio of the distance around a circle to the distance across the same circle. It is NOT 22/7 nor is it equal to 3.14128. 22/7 is not a bad approximation for such a simple division and 3.14128 is that rounded to 5 decimal places. Better, if you are going to use decimals, is 3.14159 to five decimal places or 3.1415926 to 7 decimal places. My calculator can give 12 decimal place accuracy: 3.13159265359. Some people have memorized it to several hundred decimal places and computers have been used to evaluate it to several million places. None of those are "the" value of [/itex]\pi[/itex]. (Nor are they of any particular use. Calculating $\pi$ to millions of decimal places is mainly to test [or show off] the speed of a computer.) $\pi$ is an "irrational" number and it happens that in our "base 10" numeration system, no irrational number can be written in a finite number of decimal places nor in a simple pattern.

Last edited by a moderator: Nov 1, 2008
3. Nov 2, 2008

4. Nov 2, 2008

### arjunkr

1.How to convert real problem into equation and how to solve please explain with a example
(derivative problem)?

2.How to use limit in real application ?

3.why stone will never float in water where as ship is float?

5. Nov 4, 2008

### Diffy

Halls, what country is the desert pie in?