Hey so after some great strategy by Hannah and I, I have yet again gotten the blog post.  Today in class we learned about Logarithms.Oh and thank you Mr.Wilhelm for finally changing the background... 

In an equation...

we learned that x is being expientiated and to solve this you need to log it. 

In this chapter we are learning about exponential functions, and long and behold they are one-to-one.  And what do we know about one-to-one functions??? They all have inverses!!! The inverse to exponential functions are logarithmic functions.

We know this because inverse functions are reflected over X=Y. 














Now the KEY TO EVERYTHING (also called the Definition of loga in the book) is that...

The first equation is in exponential form when the second one is in logarithmic form.

Changing equations from exponential form to logarithmic form and vice versa is fairly easy.  All you have to do is this...

(Index means exponent)










Now to solve logarithmic equations is pretty easy too.  The easiest way to do it is to change it to exponential form and we already know how to solve those.


    Given 

             Change to exponential form

               Simplify

               add 4 to both sides 






Now there are two different types of logs. 


The common log 


The natural log (the one we are gonna use most)





In the homework there were equations that looked like this
which are far less confusing than you would think. 


All this is is another way to write exponential functions.
This just means that.. 



or





Finally we learned about the graph of logarithmic functions.

Changes-
a-vertical stretch
b-higher number makes the graph grow slower
c-Shifts left/right
d- shifts up/down


So that's pretty much it for logarithms.  Thanks again to Hannah for being a very sneaky and loyal friend.
And everyone remember that finials are approaching and there is a good chance that we shall all fail.

-Jennifer Kendall