Massey logo
Home > College of Sciences > Institute of Fundamental Sciences >
Maths First > Online Maths Help > Algebra > Logarithms > The Natural Logarithm
SEARCH
MASSEY
MathsFirst logo College of Science Brandstrip
  Home  |  Study  |  Research  |  Extramural  |  Campuses  |  Colleges  |  About Massey  |  Library  |  Fees  |  Enrolment

 

Logarithms

The Natural Logarithm

The common logarithm is used in many scientific applications, such as the Richter scale. In mathematics, the most commonly used base for logarithms is the number e = 2.718281828...

loge is abbreviated to ln (read "lin") though Matlab uses log for this function.

Thus, by definition y = ex  if and only if  ln y = x

Replacing y in the second equation by ex we get  

The natural log of e to the x is x.

 

 

y equals e to the x
    is equivalent to
the natural log of y equals x.

 

Replacing x in the first equation by ln x we obtain

e to the natural log of y equals y.

 

 

    
            

It is common to write ex = exp(x).

The functions ln and exp are inverses of one another. That is, they cancel each other out.

Note   ex > 0   for any x.
Consequently,  ln x  is defined only for x>0.

Here are the graphs of ln and exp:

As y equals e to the x tends to negative infinity it approaches zero and as x tends to positive infinity the function tends to positive infinity.

Each graph is a reflection of the other with respect to the line y = x.

 

<< The Common Logarithm | Logarithms Index | Applications >>

 

   Contact Us | About Massey University | Sitemap | Disclaimer | Last updated: November 21, 2012     © Massey University 2003