Difference between revisions of "User:Temperal/The Problem Solver's Resource2"
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This is just a quick review of logarithms and exponents; it's elementary content. | This is just a quick review of logarithms and exponents; it's elementary content. | ||
===Definitions=== | ===Definitions=== | ||
− | *Exponentials: Do you really need this one? If <math>a=\underbrace{b | + | *Exponentials: Do you really need this one? If <math>a=\underbrace{b\times b\times b\times \cdots \times b}_{x\text{ }b'\text{s}}</math>, then <math>a=b^x</math> |
− | *Logarithms: If <math>b^a=x</math>, <math>\log_b{x}=a</math>. Note that a logarithm in base [[e]], i.e. <math>\log_e{x}=a</math> is | + | *Logarithms: If <math>b^a=x</math>, <math>\log_b{x}=a</math>. Note that a logarithm in base [[e]], i.e. <math>\log_e{x}=a</math> is denoted as <math>\ln{x}=a</math>, or the natural logarithm of x. If no base is specified, then a logarithm is assumed to be in base 10. |
===Rules of Exponentiation and Logarithms=== | ===Rules of Exponentiation and Logarithms=== |
Revision as of 21:50, 10 January 2009
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 2. |
Exponentials and Logarithms
This is just a quick review of logarithms and exponents; it's elementary content.
Definitions
- Exponentials: Do you really need this one? If , then
- Logarithms: If , . 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 and Logarithms
, where .
, where x is a constant.
and are undefined.