Because they are so closely related to exponential functions, logarithms have a number of applications in real life, especially when calculating the pH of any chemical substance or measuring the loudness of sounds through the use of decibels. Both of these activities, common in many different industries, require an understanding and application of logarithmic functions.
The utility of logarithmic functions extends beyond just chemistry and sound engineering. Logarithms can be applied to solve complex problems in almost any situation that also involves the use of exponential functions. For example, determining different aspects of the photographic quality of an image can be broken down into logarithmic pieces. This is possible because information about the photograph, such as the ratio of incident light to transmitted light, can be expressed in mathematical ways. These ratios and variables can then be manipulated with logarithms to extract information about the photo and ensure its quality.
Logarithms are also invaluable in the real-world finance industry. Through the use of logarithmic and exponential functions, financial experts can determine the value of money that has been invested or loaned over time, with a number of different fluctuating variables. For finance companies, it is important to know the future and present values of sums of money. They utilize the power of logarithmic equations to efficiently estimate these values.