What is log and how it is used?
Answers
Logarithms or logs are a part of mathematics. They are related to exponential functions. A logarithm tells what exponent (or power) is needed to make a certain number, so logarithms are the inverse (opposite) of exponentiation. Historically, they were useful in multiplying or dividing large numbers.
An example of a logarithm is {\displaystyle \log _{2}(8)=3\ }{\displaystyle \log _{2}(8)=3\ }. In this logarithm, the base is 2, the argument is 8 and the answer is 3.
The most common types of logarithms are common logarithms, where the base is 10, and natural logarithms, where the base is e ≈ 2.71828.
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Hey mate here is ur answer =
Logs or logarithms --->
☆Definition =one of a series of numbers arranged in lists (tables) that allow you to solve problems in mathematics by adding or subtracting numbers instead of multiplying or dividing.
☆A logarithmic function can be used to transform an exponential function into a linear expression. For example by applying Ln to both sides we get a linear expression.
☆Who developed it?
John Napier Developed logarithm in 1614.
☆Application in mathematics =
The logarithm is taught very early on in one’s mathematical career due to the enormous amount of application it has. I will list a few applications, but keep in mind that there are so many more applications that depend on the context of the problem you are solving for. Not only that, there often times is a need for the log in the process of evaluating a limit, derivative or even integral.
☆Some common uses =
☆pH levels in chemistry. The value of pH can be quite small, so the log is used, since it is base 10, to create a range for very small values.
☆Interest with banking
☆Half life of a radioactive material
☆Deriving the charge of a capacitor
☆Range for loudness. This follows the same logic as with pH.
☆Earthquake intensity. Same as pH
In short it is a useful base for many other chapters in mathematics.
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