The cache is not at the posted coordinates. Now let's have some fun with logarithms!
Back in the olden days before computers were small enough and cheap enough to carry around in your pocket, doing mathematical calculations was tedious work. Naturally, this work was often delegated to women. The women who did this work were called “computers”. In some fields (such as astronomy) multiplying large numbers was particularly onerous. Fortunately around the seventeenth century logarithms came into use. A logarithm answers the question – how many of one number do we multiply to get another number?
For example
4 x 4 x 4 = 64
The number 4 is multiplied 3 times to get 64. The notation for logarithms is written
logb x = y
Where b is the base. In the above example the base is 4.
X is the product. In the above example the product is 64.
y is the exponent. In the above example the exponent is 3.
So plugging in the numbers we get
log4 (64) = 3
Which is the same as
43 = 64
Logarithms with a base of 10 are “common” logarithms.
log10 (72) = 1.857332
Which is the same as
101.857332 = 72
So, who cares? Well, if your job required you to multiply large numbers and all you had at your disposal for the task was a piece of paper and a quill; logarithms enable you to multiply two numbers by simply adding their exponents.
So, how to find the cache? All you need to do is fill in the decimal minutes portions of the cache location.
N 48° __ __.__ __ __ W 123° __ __.__ __ __
The latitude portion is easy. Simply find the common logarithm for 1089 and round to 3 decimal places.
The longitude portion is going to require a bit more work.
First arrange the squares in the following grid such that equivalent equations align along the touching edges. All bases are positive numbers. You can find a printable version in the gallery.
Once the squares are rearranged, read off the center number of each square in order left to right, top to bottom.
__ __ __ __ __ __ __ __ __
Finally, find the common logarithm for the above number and round to 3 decimal places.
A FTF Geocoin awaits the FTF.
