Answer:
In mathematics, we are currently studying the topic of logarithms. Log, simply put, is the inverse of exponents and is generally used to solve calculations that have rather large powers. This topic is quite complex, with a heavy dependance on scientific calculators to solve the majority of problems – in our modern society, all log values are easily found with the use of a calculator. Keeping this in mind, one is left to ponder how mathematicians of the 1600’s and 1700’s were able to solve such complicated mathematics without such technology. Firstly though, a brief history regarding logarithms. According to SOSMATH (1999), the method of logarithms was first publicized by a man known as John Napier, in 1614. However, at a similar time, a Swiss man named Joost Burgi had also been working on a concept similar to the idea of log. These two men had different ideas regarding log. Napier’s method of logarithms was heavily related to algebra, while Burgi’s approach was much mor geometric. Although these men are somewhat credited with the discovery of logarithms, the possibility of defining exponents with the use of logarithms was first proposed by a man named John Wallis in 1685. Overall though, the original discovery of logarithms can be contributed to Napier and Burgi – it was Wallis who discovered its uses in terms of exponents. Now, how did people use log to solve problems, when they did not have a the technology that is present today? Essentially what they did was to use something called a log table. A log table, simply put, is a list of common logarithms (with base 10) for numbers between 1 and 10. Therefore, mathematicians simply re-wrote their complicated logarithms into logarithms with base of 10. Thus, they could use the log table, find their logarithm, and the table would contain that log value converted into a number. In relation to this, when solving these difficult logarithms, mathematicians followed a number of rules, known as the law of logarithms. Here are a few of those rules.
Log(ab)=log(a)+log(b)
Log(a/b)=log(a)-log(b)
An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.
Below, I have tried one of these ‘difficult’ logarithms and attempted to solve it without my calculator, thus using only the log table and my own mind. I have outlined the steps I took next to my calculations.
