# Uses of Logarithms in Computers

Logarithms have been an important part of mathematics since 1614. Mathematicians and computer programmers use logarithmic exponents because it simplifies complex mathematical calculations. For example, 1000 = 10^3 is the same as 3 = log101000. Computer developers use logarithms in computer function formulas to create specific software program outcomes, such as the creation of graphs that compare statistical data.

### Computer Modeling

Computer modeling creates comparison models that predict outcomes based upon mathematical statistical information. In computer modeling, logarithms may represent any subject we wish to compare, such as the brightness of light or earthquake intensities. When a computer measures magnitudes, it creates a logarithmic scale. Computers analyze exponential processes such as the spread of an epidemic by the plotting sets of logarithmic measurements. The process creates a modified logarithmic curve called a logistic.

### Computer Imaging

Logarithms used in computer imaging align pixels, organize colors and help computers manipulate photographs for enhancement, merging or comparison. After the creation of a digital image, the photographed information converts into small sections of color called pixels. For a computer to recreate an image, it organizes the red (R) green (G) blue (B) values for each pixel and transforms them into two dimensional color pairs, such as G/R, B/R. Each pairing signifies a specific mathematical logarithm that allows the computer to translate and align each pixel into the photographed image.

### Cryptology

Discrete Logarithms are an important part of creating effective computer cryptosystems. The variable nature of the numerical key exchanges in certain logarithmic formulas allows cryptologists to develop computer security systems that restrict user access and act as a sieve barring specific security attacks.

### Application Development

Engineering, business and science applications use logarithmic functions. In addition, programing languages, such as C and C++, use logarithmic formulas to establish non-linear relationships and to define number inputs into calculations -- for example, the use of LOG10 natural logarithms for numerical input functions to the tenth power in the development of MS Windows products. Logarithmic functions used to calculate real arguments outputs in a computer program must be greater than zero.

### References & Resources

- University of Montana: Chopping Logs: A Look at the History and Uses of Logarithms
- Microsoft Developer’s Network: Log Function Windows Scripting 5.8
- MIT Laboratory of Computer Science: Lecture Notes on Cryptography; Shafi Goldwasser and Mihir Bellare; August 2001
- Oak Road Systems: It’s the Law Too — the Laws of Logarithms
- University of California: Multi-subject Diffusion MRI Tractography ... Approach
- Simon Fraser University: Invariant Image Improvement by sRGB Colour Space Sharpening
- Richland Community College: Exponential and Logarithmic Models