Given X and Y, you wish to find X*Y using logarithms.
You can take logs to any base, z. For common logs, the base is 10; for natural logs it is e (Euler's number).
Logarithms turn multiplication into addition, which is much faster. The same applies for division, except that the logs are subtracted. Using logarithms, finding roots or powers is easy. For example, the square root of a number can be found using 1/2 times the logarithm (plus one more step). Finding square roots is something that happens often in algebra. If you did not have a calculator, square roots would be hard without logarithms.
Logarithm tables help you work with logarithms without using a calculator. Calculating a logarithm can be a long process. A table eliminates the need to perform extra math. If you need a specific logarithm, you simply look it up. The calculator was invented in the 1970's. Before that, people used slide rules or tables of logarithms. Using the tables of logarithms, you could perform multiplication, division, find roots or powers - and do all of that fairly easily.
Before the invention of the calculator, people needed to perform math by hand. Using tables of logarithms greatly sped up the common tasks of multiplication, division, powers and roots. Today, people use devices or scales that are based on logarithms. Music volume is based on a logarithmic scale. Every time you turn the volume up, you are doing something based on logarithms. Earthquakes are based on a logarithmic scale. Every time that you hear about an earthquake on the news, the earthquake is described in reference to a scale based on logarithms. Earthquakes happen daily all over the world.
Before the invention of the calculator, people needed to perform math by hand. Using tables of logarithms greatly sped up the common tasks of multiplication, division, powers and roots. Today, people use devices or scales that are based on logarithms. Music volume is based on a logarithmic scale. Every time you turn the volume up, you are doing something based on logarithms. Earthquakes are based on a logarithmic scale. Every time that you hear about an earthquake on the news, the earthquake is described in reference to a scale based on logarithms. Earthquakes happen daily all over the world.
Yes. The invention of the electronic calculator made using logarithms unnecessary for many of the more common usages.
To solve 239 by 47 using Napier's Bones, you would set up a grid of sticks with numbers arranged in a specific pattern. Then, by following a set of multiplication and addition steps using the numbers on the sticks, you can calculate the answer. This method allows for quick multiplication by breaking down the process into simpler steps.
The answer will depend on the detailed nature of the question.
You can get from 6 to 18 using multiplication by multiplying it by 3!
Logarithms are actually an area of mathematics. Using logarithms one might ask the question, "what is the logarithm of 5 (base 10 being assumed)" And the answer would be, you would raise 10 to the power 0.698970004 to result in 5.
You could take logarithms to base 10.
I memorized the multiplication table in fourth grade.
Using multiplication 40 times 45 = 1800