User:Temperal/The Problem Solver's Resource2: Difference between revisions

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The Problem Solver's Resource

Introduction	Other Tips and Tricks	Methods of Proof	You are currently viewing page 2.

This is just a quick review of logarithms and exponents; it's elementary content.

Exponentials: Do you really need this one?
Logarithms: If $b^a=x$ , $\log_b{x}=a$ . Note that a logarithm in base e, i.e. $\log_e{x}=a$ is notated as $\ln{x}=a$ , or the natural logarithm of x. If no base is specified, then a logarithm is assumed to be in base 10.

$a^x \cdot a^y=a^{x+y}$

$(a^x)^y=a^{xy}$

$\frac{a^x}{a^y}=a^{x-y}$

$a^0=1$ , where $a\ne 0$ .

$\log_b xy=\log_b x +\log_b y$

$\log_b x^y=y\cdot \log_b x$

$\log_b \frac{x}{y} =\log_b x-\log_b y$

$\log_b a=\frac{1}{\log_a b}$

$\log_b b=1$

$\log_b a=\frac{\log_x a}{\log_x b}$ , where x is a constant.

$\log_1 a$ and $\log_0 a$ are undefined.

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 <math>\log_1 a</math> and <math>\log_0 a</math> are undefined.
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