Do Logarithms play any major part in being able to do calculus?

In summary, logarithms and the number e are closely related to calculus, with the definition of ln() and 'e' being based on calculus. The definition of ln(a) is the integral of 1/x from 0 to 'a'. Additionally, 'e' is an irrational and transcendental number. Its value can be approximated by (1+1/n)^n for large values of n, and it can also be expressed as a limit. Knowledge of logarithmic rules and exponents is important in calculus.
  • #1
thharrimw
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do Logarithms play any major part in being able to do calculus?
 
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  • #2
More the other way around - the definition of ln() and 'e' are based on calculus.
 
  • #3
mgb_phys said:
More the other way around - the definition of ln() and 'e' are based on calculus.

but how are they based on calculus?
 
  • #4
The definition of ln(a) is the integral of 1/x from 0 to 'a'
 
  • #5
mgb_phys said:
The definition of ln(a) is the integral of 1/x from 0 to 'a'

From 1 to a, not 0.
 
  • #6
do'h sorry
 
  • #7
mgb_phys said:
The definition of ln(a) is the integral of 1/x from 0 to 'a'

Your definition not everyones. It would be fair to say that many standard definitions use some concept of limit (i.e. use calculus) and many that do not use inequalities that are very limit like. Also we would like log to be continous, a calculus (or topology) concept.
 
  • #8
ok so one of my teachers told me that the number e came from (1+1/n)^n as n Approaches infinity but now do you get 2.71828182846... from (1+1/n)^n
 
  • #9
Try it! Just put in the first few terms.
To answer your original question, 'e' comes up in a few standard calculus solutuions.
And obviously knowing the rules about multiplying and adding exponents comes into a lot of calculus.
 
  • #10
mgb_phys said:
Try it! Just put in the first few terms.
To answer your original question, 'e' comes up in a few standard calculus solutuions.
And obviously knowing the rules about multiplying and adding exponents comes into a lot of calculus.
is e a ratio?
 
  • #11
No, it's an irrational number, that means that it can't be written as a/b.
Actually it's also a trancendental number - meaning it can't be written as any equation with a finite number of terms, just like pi.
 
Last edited:
  • #12
ok so the number e [tex]\approx[/tex] (1+1/n)^n
 
  • #13
I suppose a mathematician would say that e was exactly (1+/1n)^n for infiinite 'n'
 
  • #14
thharrimw said:
ok so the number e [tex]\approx[/tex] (1+1/n)^n
Not until you tell us what n is! Yes, for very large n, e is approximately that.

mgb_phys said:
I suppose a mathematician would say that e was exactly (1+/1n)^n for infiinite 'n'
Not unless he/she were speaking very loosely. 'n' is never infinite. What is strictly true is that [itex]e= \lim_{n\rightarrow \infty}(1+ 1/n)^n[/itex].
 

Related to Do Logarithms play any major part in being able to do calculus?

1. What is a logarithm?

A logarithm is an inverse function to an exponential function. It is used to solve exponential equations and is commonly represented as logb(x), where b is the base and x is the value.

2. How are logarithms used in calculus?

Logarithms are used in calculus to simplify complex mathematical expressions involving exponents. They are also used to solve equations involving exponential growth and decay, which are important concepts in calculus.

3. Can calculus be done without using logarithms?

Yes, calculus can be done without using logarithms. However, logarithms do play a major role in simplifying and solving equations, making the process more efficient and easier to understand.

4. What is the relationship between logarithms and exponential functions in calculus?

The relationship between logarithms and exponential functions in calculus is that they are inverse functions of each other. This means that the logarithm of a number is the exponent needed to raise the base to get that number.

5. Are logarithms used in other areas of mathematics besides calculus?

Yes, logarithms are used in many other areas of mathematics, such as statistics, finance, and physics. They are also commonly used in computer science and engineering to solve complex equations and algorithms.

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