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.