So you are tasked with discovering how to use the properties of logarithms and a table of common logarithms to multiply, divide, and exponentiate two numbers just like folks did before calculators and slide rules. First, try to figure it out using your own brain. If that fails, try enlisting the help of someone else's brain: the Internet, your really smart friend, your teacher. Your grade will not come from the completion of this sheet. You will have to do 3 similar problems in class for your project grade, so make sure you really understand how these methods work.
Realize that you cannot use a calculator on this project. So to evaluate a particular logarithm, use the handy Common Log Table, which I found somewhere on the Internet. Nowadays, we would just find the logs of numbers by pressing buttons on our calculators, but it wasn't always so. You may notice that this table of logs is for numbers 1.0 to 10.0, but the numbers you have to multiply and divide are in the hundreds. I wonder how you will overcome this shortcoming.
Despite sounding like a piece of cabin furniture, log tables, as Professor Bowley explains, helped increase the speed and accuracy of calculations in the olden days. Numberphile. Duration_5_09
A continuation of the previous video, Professor Bowley explains how John Napier developed the first log table. Numberphile. Duration_5_43
The Post Apocalyptic Inventor demonstrates how to use and make Napier's Bones, another invention of John Napier that functioned as a precursor to a digital calculator. Well, a calculator that only does multiplication and division. Note that these rods do not use logarithms. Duration_13_48