Details of logarithmic calculations?

In summary, the conversation is about someone wanting to know how logarithmic and cosine calculations are done. The conversation mentions the use of Taylor's Series for logarithmic calculations.
  • #1
kiru
22
0
From where I can get the details of lograthmic calculations?How the values are found?and on what basis?
 
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  • #2
Do you want to know for instance how [tex]\log{3}[/tex] is found? That kind of calculation?
 
  • #3
Jameson said:
Do you want to know for instance how [tex]\log{3}[/tex] is found? That kind of calculation?
Actually I want to know this:We know that log{2} is 0.3010.How it is calculated?
 
  • #4
kiru said:
Actually I want to know this:We know that log{2} is 0.3010.How it is calculated?

I would have the same question + how cosines are calculated.
 
  • #5
There are a variety of ways.

The simplest is to use "Taylor's Series". It can be shown, in Calculus, that for x between 0 and 2, ln(x)= (x-1)- (1/2)(x-1)2+ (1/3)(x-1)3-...- ((-1)n/n)(x-1)n+... That infinite series does not converge very fast but it will give close to the correct value eventually.
 

1. What is a logarithm?

A logarithm is a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. In other words, it is the inverse of exponentiation.

2. How do you calculate logarithms?

Logarithms can be calculated using a scientific calculator or by using logarithm tables. To find the logarithm of a number, you need to know the base of the logarithm and the number itself. The formula for calculating logarithms is logb(x) = y, where b is the base, x is the number, and y is the logarithm.

3. What is the difference between common logarithms and natural logarithms?

Common logarithms, also known as base 10 logarithms, use the number 10 as the base. Natural logarithms, on the other hand, use the number e (approximately 2.718) as the base. Natural logarithms are commonly used in scientific and mathematical calculations, while common logarithms are more useful for everyday calculations.

4. How are logarithms used in science?

Logarithms are used in science to simplify complex calculations involving very large or very small numbers. They are also useful in converting between different units of measurement, such as decibels in acoustics or pH in chemistry. In physics, logarithms are used to describe exponential growth and decay.

5. What are some common properties of logarithms?

Some common properties of logarithms include:

  • The logarithm of a product is equal to the sum of the logarithms of the individual factors.
  • The logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.
  • The logarithm of a power is equal to the exponent multiplied by the logarithm of the base.
  • The logarithm of 1 is always 0.
  • The logarithm of a number greater than 1 is positive, while the logarithm of a number between 0 and 1 is negative.

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