This problem was solved in 1594 by a Mathematician from Scotland, known as John Napier, who introduced a set of logarithmic numbers. (Nagel, 2002, 2006) Today, they are used in modern scientific methods as well, such as calculations for computer science applications and algorithms. Finding out the efficiency of a certain algorithm, the time it takes to solve particular instructions etc. other than that, for many years, logarithms have been used in physics, chemistry, biology in calculating statistical data and values. Logarithms are used in graphical representation of the collected data and can also be used to forecast a trend based on the given data. In the field of engineering, exponentials can give you a hard time determining correlations between events and factors. In such cases, a logarithm can make the problematic function linear and provide a pretty accurate approximation. This makes solving it easy. The graphical representations of logarithmic functions can be much easier to analyze than complex ones and give a better understanding. An example would be of biology, in which the growth of an enzyme is being monitored. Suppose the function provided is:
Converting a logarithmic function into an exponential function can be done in a simple way. A logarithmic function is the reflection of an exponential function in the line y = x. ...
An example would be of biology, in which the growth of an enzyme is being monitored. Suppose the function provided is:
Y = ln x (9.5), where x is the variable that strains the growth of the enzyme. The graph for it would look like:
The graph provides a linear and simple representation, without the use of logarithm, this could be a very problematic function to deal with.
Logarithm to Exponential
Converting a logarithmic function into an exponential function can be done in a simple way. A logarithmic function is the reflection of an exponential function in the line y = x. for example, the equation we took above, y = ln x (9.5) would become y = ex(9.5). the graph for the exponential function would look like:
Here, we clearly see that both graphs are laterally inverted.
Y = ln x(9.5)
After reflection in the line y = x;
X(9.5) = lny
Now recall that if ln x = y, then x = e y
Therefore if ln y = x, then y = e x
so; y = ex(9.5)
1. L. Bostock, S. C. (1990, 1994, 2000). Core Mathematics for Advanced Level. Cheltenham: Nelson Thornes.
2. Nagel, R. (2002, 2006). Logarithm. Retrieved June 20, 2008, from enotes.com Encyclopedia of Science: http://www.enotes.com/uxl-science-encyclopedia/logarithm
3. Zorn, W. (n.d.). Function Grapher Online. Retrieved June 20, 2008, from walterzorn.com: