User:Temperal/The Problem Solver's Resource2
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Exponentials and Logarithms
This is just a quick review of logarithms and exponents; it's elementary content.
- Exponentials: Do you really need this one? If , then
- Logarithms: If , then . Note that a logarithm in base e, i.e. is denoted as , or the natural logarithm of x. If no base is specified, then a logarithm is assumed to be in base 10.
Rules of Exponentiation
, where .
These should all be trivial and easily proven by the reader.
Rules of Logarithms
This can be seen by writing as .
, where x is a constant.
All of the above should be proven by the reader without too much difficulty - substitution and putting things in exponential form will help.
and are undefined, as there is no such that except when (in which case there are infinite ) and likewise with .