Why are logarithms used?

Question

also, Where would u apply loge and log10?

Answer 1

Currently logarithms are useful when the scale of something needs to grow quicker than in usual arithmetic increments.

For example, the earthquake scale is logarithmic. An earthquake of 2 is not twice as strong as an earthquake of 1; it is more than twice as strong. Use of a log scale means you can still talk about earthquakes of 1, 2 , 3, etc.

Logarithms are also used computationally in problems with exponents. How many years will it take an investment to double if the interest rate is 5%, is a problem solved with logarithms.

Base 10 is used in courses prior to calculus. Base e is used in higher level courses, and in real-world computation. I do use base e, but I never use base 10.

By the way, e appears all over higher mathematics, in ways that are totally unexpected.

Answer 2

Log10 is the power that ten is raised to, to get a given number. i.e. log10 (100) = 2, log10 (1000) = 3 etc. They are based on the principal that log (x*y) = log x + log y
So before the computer and even before desktop calculator, mathematical tables were produced giving values for logarithms to facilitate multiplication (because addition is easier). Log 10 is used because 10 is our base denomination.

Answer 3

Because some natural phenomena operate on logarithmic scales. The most commonly known one are earthquakes--it doesn't really work to measure earthquakes on a linear scale, because their power varies so greatly. It's much easier to say "3.0 on the Richter scale vs. 6.0 on the Richter scale" than "1000 on the Richter scale vs 1000000 on the Richter scale"--but that is what you would have to do without a logarithmic scale.

Log base e is even more important--a vast number of physics problems will eventually involve the use of natural logarithms. One could almost say that Log base e is the "normal" type of logarithm, in the sense that it is the one most connected to the actual world, while log base 10 is usually used because it's a human convention (related to our base 10 number system).

Answer 4

Base e logs are used in all work related to calculus. Base 10 logs used to be used for doing multiplication, division and exponentiation before the days of calculators, and are used to define pH values relating to acidity and alkalinity in Chemistry.

Answer 5

I believe if you were going into a field that requires graphs and utilities it would apply.

Answer 6

they are interconvertible.generally in plain computation we use base 10.in calculus we use base e