BOBlog

Good Morning bloggers! I could not sleep so what better time to do my blogging on blog post! :)

This unit was exponents and logarithms. It started of as a scary subject but as it went on I did not find it terribly difficult and understood things quite well and quickly.  Time for a review!

Alright, first thing to say is that a logarithm is an exponent!!!! I have not forgotten that yet and I don't plan on it!!!

The basic form an exponential equation is A^B=C where A is the base, B is the exponent and C is the power. Ex. 95^2=9025....... (It's over 9000!!!!! XD sorry for that)

The basic form for a logarithmic equation is logAC=B where A is the base, C is the power and B is the exponent. 

A logarithm is the inverse of the exponential function. For the exponential function you "feed it" exponents and it gives you powers where as a logarithmic function you "feed it" power and it gives you exponents. (I'm really tempted to make more over 9000 references XD)

Now there are several laws when working with logarithms you should know. There is the Product law, Quotient law, Power law, and Change of Base law.

Product law: loga(MN)=logaM+logaN 

Quotient law:loga(M/N)=logaM-logaN

Power law:loga(M^N)=NlogaM

COB law:logN(M)=loga(M)/loga(N)

There is also the mystic and all powerful number e!! Check out the history of it here!! Anywho... Using the number we we can make The exponential function and The logarithmic function, being f(x)=e^x and f(x)=ln(x) respectively. (ln is the same as loge)

Woah! Almost forgot but there is some things on exponential growth and decay as well! Now if I remember correctly we can use the Pert formula of A=Pe^rt where A is equal to the final amount, P is what you start with, e is e, r is the rate and t is time in years. With this little bad boy of an equation we can solve INTERESTing problems.....XD.... as well as we can calculate half lives with it. If all else fails you can whip out A=P(1+r/n)^tn where n is the number of times we compound the principle value per year. As a side note, if you take 1 dollar and compound interest on it at 100% for a year and you did it enough times, like more than once per second it would eventually plateau out at number e!

One more thing, I remember Mr K. going over those modeling questions there are 2 formulas for that!! A=AO(model)^t where A is the final amount of what ever at the end of the time, AO is the beginning amount of what ever at the start of the time, the model is how much it has either grown or decayed and t is the time that has passed. This is used when you have minimal information.

If you have a lot of info then you may use A=AO(m)^t/p where A is the final amount of what ever at the end of the time, AO is the beginning amount of what ever at the start of the time, m is the growth rate, p is the time required to multiply by m once and t is equal to time.

Well i think that about raps it up. I am off to sleep because I am exhausted.