User:Temperal/The Problem Solver's Resource2

The Problem Solver's Resource

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? Logarithms: If , . Note that a logarithm in base e, i.e. is notated 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 =a^{x-y}$$ (Error compiling LaTeX. Unknown error_msg)a^0=1a\ne 0\log_b{xy}=\log_b{x}+\log_b{y}$$ (Error compiling LaTeX. Unknown error_msg)\log_b{x^y}=y\cdot \log_b{x}$$ (Error compiling LaTeX. Unknown error_msg)\log_b{\frac{x}{y}}=\log_b{x}-\log_b{y}$$ (Error compiling LaTeX. Unknown error_msg)\log_b{a}=\frac{1}{\log_a{b}}$$ (Error compiling LaTeX. Unknown error_msg)\log_b{b}=1$$ (Error compiling LaTeX. Unknown error_msg)\log_b{a}=\frac{\log_x{a}}{\log_x{b}}\log_1{a}\log_0{a}$ are undefined.