Last class we learned more about logarithms."The Change of Base Therom" the last log law.
logb^n=loga^n/logab
ex) heres a little rule
log (x + 3) = IS ABSOLUTELY NOT- logx + log3
instead, it becomes:
log(2(3^x)) = log5
log2 + log3^x = log5
log2 + x * log3 = log5
x * log3 = log5 - log2
x = log5 - log2 / log3
x = .8340437671

Yesterdays class we learned logarithmic functions.
y=log6x if x=by(y as the exponent) y is the logarithm, b is the base and x is the argument.
Logarithms are exponents.
We did an example like, find log2(subscript)8=3 in exponential form. 2to the 3=8
2 to the ?= 16 9 to the ?=3
2 to the 4=16 9 to the x=3
log2(being the subscript)16=4 (3 to the 2)=3 therefore 2x=1 x=1/2
then: 2 to the ?=1/4 2x=4 to the exponent -1 2x=(2 to the exponent 2) -1(exponent) therefore x=-2 therefore log2(subscript)(1/4)= -2

Today in class we learned about expotential functions. We had learned lots of it in grade ten precalc. First we sketched out some simple graphs, and talked about them a bit, like what would happen if you changed the a or b value, ect..Then we did some observations , like D= all reals, graphs have no x intercept(no verticaln shifts). And then we did some examples, which were quite easy.

Yesterdays class was a catch up period, one of my favs. I worked on some accelerated math, and got 79%, wasn't bad, but I have to do some objectives over again which sucks. I was very happy we got a catch up block because I am somewhat behind in this class. And stressing over this math test comming up on thursday.

Today in class we did some more practice/considerations with identities. We learned about EXTRANEOUS roots.- "they are answers that look good on paper but practically don't make sense".
When we are doing our questions, all solutions must be checked for validity. In an equation you want to bring everything to one side, and when you have a question like cos(x)+1=sqare root thre sin(x), you always want to sqare both terms to get rid of the radical.

Today in class we learned how to simplify. Completely. And learned techniques to assist "proofing" idenities. There was eight different techniques. Such as reduce/simplify, work each side independently to some intermediate expression, DO the multiplication/subtraction of the rational expressions, Simplify GCF'S ALWAYS, FACTOR, try multiplyinf both numerators/ denominators by same expression, and lastly, if possible rewrite all trig. functions as sin(x) or cos(x); look for patterns.
And we learned to prove by LHS and RHS. I find it kind of complicating,but hopefully I will catch on.

Last class we got a CATCH UP CLASS! I especially love these days. Because I usually have a lot of catching up to do. I worked on exercise 12 that is due for monday. I unfortunatley did not finish, but I will finish it sometime this weekend.