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Common logarithm

Logarithms

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Calculus
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Fields of mathematics
Mathematics
Logarithms
Mathematical analysis
Binary operations
Additive function
Exponentials
Napierian logarithm
Common logarithm
Natural logarithm
John Napier
Exponentiation
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logarithms

Many students in high school and in college have a difficult time with logarithms. In many cases, they memorize the rules without fully understanding them, and they sometimes even manage to squeak by a course. Why waste their time on these archaic entities; they are never going to see them again. Wrong! Just when the student breathes a sigh of relief to be done with logarithms, they encounter them again in another course. They are now in trouble because the second encounter with logarithms is at a more sophisticated level. Without an understanding of the basics, the student is doomed to blindly stumble through and fail the course. You have our sympathy and you have our solution. We at S.O.S. Math want you to succeed.

Logarithims

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Algebra
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Logarithms
Common logarithm
Natural logarithm
Technology
For any base, the logarithm function has a singularity at . In the above plot, the blue curve is the logarithm to base 2 (), the black curve is the logarithm to base (the natural logarithm ), and the red curve is the logarithm to base 10 (the common logarithm, i.e., log, ). Note that while logarithm base 10 is denoted in this work, on calculators, and in elementary algebra and calculus textbooks, mathematicians and advanced mathematics texts uniformly use the notation to mean , and therefore use to mean the common logarithm. Extreme care is therefore needed when consulting the literature. The situation is complicated even more by the fact that number theorists (e.g., Ivić 2003) commonly use the notation to denote the nested natural logarithm .
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