Pre-Calculus B, 2nd Hour, Winter 2012: Logarithms

Friday, January 13, 2012

~Logarithms are the inverses of exponentiation.

KEY TO EVERYTHING!

$a^x=y \rightarrow log_{a}y=x$
Example:

$log_{2}8=x$
$2^x=8$

$x=3$

When the base numbers match, you can set the exponents equal to each other.

$5^x=125$
$5^x=5^3$

$x=3$

$\frac{1}{32}\cdot 4^{x}=2^{x}$

$2^{-5}\cdot (2^{2})^x=2^{x}$

$2^{-5}\cdot 2^{2x}=2^{x}$

$2^{2x-5}=2^{x}$

$x=2x-5$

$x=5$

Log- The Common Log with a base of 10

Ln- The Natural Log with a base of e

Logarithm Graph

$y=alog_{b}(x-c)+d$

Pre-Calculus B, 2nd Hour, Winter 2012