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Published online by Cambridge University Press: 05 June 2012
My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help in astronomy, viz. the logarithms, but, my lord, being by you so found out, I wonder nobody found it out before, when now known it is so easy.
Briggs to NapierThe aim of this chapter is to explain what logarithms are, and to discuss the ways in which they are used. Some of the material is not very easy to grasp, but you do need to have an understanding of this area. Even for people who already are familiar with logarithms there is probably something new in this chapter.
Logarithms
A logarithm is a way of writing one number (x) expressed as a power (index) of a second number (y) which is called the base, and which must be a real number >1. Some examples should make clear what this means. The number 8 is 23, and therefore if 2 is used as the base we can write: log2 8 = 3; in words this is to say that the logarithm of 8 to the base 2 is 3. Now, if 8 rather than 2 had been used as the base then log8 8 = 1 (8 = 81). If 64 were the base, then 8 (=√64) would be expressed as log64 8 = 0.5.
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