How Logs Work – the easy way!
In Year 9 I had a maths teacher who was really good at music and OK at maths. Anyway, we had a visiting “inspector” type of man one day who had come from overseas and came to see our maths class. The topic we had been working on was Logarithms (Logs) and we had been doing Log problems for well over a week. The visitor asked the class if anyone could tell him what a Logarithm was. Nobody had the answer. I was so embarrassed to think that we had been learning something for so long and we we couldn’t even explain what it was! When I started teaching Logarithms I was determined that my classes should know how to define them. First I wrote a typical Log equation on the board, e.g.,
Of course, we read this as, “The log of 8 to base 2 equals 3“. The base is 2, the power (or exponent) is 3 and the number is 8.
Now, in order to better see how this works I added the following arrows, starting with the base we are working with – in this case base 2 (which simply means a number system of 0 and 1 – the same number system you are using on your computer right now. Another way to imagine this is to think of aliens visiting the earth. When you get over the shock of seeing these creatures for the first time, you notice that they only have one digit (finger) on each hand. They would, no doubt, also use a base 2 number system! We use a base 10 number system because we have ten fingers. OK, so my log explanation was much easier with the arrows;
Now, read this with me, starting at the 2: “2 to the power of 3 equals 8” That is the same as saying, “The log of 8 in base 2 equals 3”. How easy this made working with Logs! Here is both ideas put together (mathematically);
Note: When working on Log problems like the one above I would always recommend that you add the arrows (as used in the first example). This helps get the problems right until you have the concept firmly cemented. Hope this helps you understand Logarithms! Here is another worked example;