Section 5.3 - Logarithms!

This section was on logarithms! Logarithms are basically the inverse of an exponential equation. Literally, it means ratios of numbers.

exponentiation is what is being done to X in this case.


To solve, we need to undo what is being done to X, which is a logarithm :)

Mr. Wilhelm's KEY TO EVERYTHING!

That is how to rewrite an exponential function as a logarithmic function. With this, we can solve exponential equations that would otherwise be unsolvable!

This is how you might apply a logarithm to an exponential function. As you can see, Y=1,000  A=10   and X=3

The key to everything is as easy as that :)

Special Logarithms!

When it is just written "log" with no subscript, it is implied that it is log10 -- COMMON LOG!

When it is written ln, it is implied that it is loge -- NATURAL LOG!

How to graph a logarithm!

A few other little tidbits to know:

since the domain of an exponential function is (-∞, ∞), so thats the RANGE of a logarithm

the range of an exponent is (0, ∞), so thats the DOMAIN of a logarithm. (unless it has been moved by the C value)

*Exponents and Logarithms are 1 to 1*

Sorry, there are no pretty logarithm pictures on the internet :(

Links and stuff:

http://www.themathpage.com/aprecalc/logarithms.htm

http://www.sosmath.com/algebra/logs/log1/log1.html

http://www.purplemath.com/modules/logs.htm

http://www.shodor.org/unchem/math/logs/index.html

http://www.youtube.com/watch?v=mQTWzLpCcW0

And, just for old time's sake :

Nonagon Song - http://www.youtube.com/watch?v=x5ohtlewREI

One Dozen Monkeys -http://www.youtube.com/watch?v=2qdql9vsWWM&feature=related

Hope this helped and made logarithms a little less unbearable :)

Bye, Katie