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 

1.2- Exponents and Radicals

Yesterday we learned about the rules of exponents. These rules are as follows:

The quotient rule above is the example for when the larger exponent is in the numerator, but if the larger exponent is in the denominator you would put the base 'x' to the power of n-m all over one. That would look like this 

This next picture is an example of the work that lets you get from to , where .

       

We also learned how to change exponents into radicals and vice versa. But before I get into that I will go over the names of a radical's parts.

Now, I will go into making exponents into radicals, and radicals into exponents.

This shows where the exponent's numerator and denominator go when it's made into a radical.

This shows where the radical's index and the radicand's exponent go when it's made into an exponent.


The diagram below shows some examples of turning radicals into exponents:

Hope you like the post and sorry its so long.

Bye,

and Go Blue,

Alex Hackert