1. Logs
1.1. Definition
1.1.1. the exponent that I must take the base to in order to get the arguement
1.1.1.1. notes from 3/14
1.2. parts of a log
1.2.1. log(base as subscript)(argument)
1.2.1.1. "log base _ of _ is _"
1.2.1.1.1. notes from 3/14
1.3. without calculator
1.3.1. make it base to the x power equals the argument
1.3.1.1. exponent chart
1.3.1.2. notes from 3/14
1.4. with calculator
1.4.1. hit math alpha math then plug in base and argument
2. More equations with logs
2.1. logbx = y -> b^y=x
2.1.1. Paper notes from 3/15
2.2. Isolate base
2.2.1. inverse operations to cancel out
2.2.1.1. PEMDAS
2.2.1.1.1. paper notes 3/15
2.3. use logs
2.3.1. if exponent is equation, find the log that it will be equal to
2.3.1.1. paper notes 3/15
3. Applications
3.1. half life
3.1.1. how long it takes the thing to half
3.1.1.1. P=P0(.5)^t/h
3.1.1.1.1. packet notes 3/21
3.1.1.1.2. P0 is starting amount and t is time passed and h is half life
3.2. Exponential model: ab^x
3.2.1. a= starting value
3.2.2. b=growth/decay factor
3.2.2.1. Notes from 3/19
3.2.2.2. growth = 1 + r & decay = 1 - r
3.2.3. x = time passed
3.3. Continuous
3.3.1. change exponentially at a continuous rate
3.3.1.1. P=P0e^rt
3.3.1.1.1. packet notes 3/21
3.3.1.1.2. P0 is starting point and e is Euler's number and r is growth/decay rate and t is time passed
4. Graphing
4.1. Parent Function
4.1.1. b^x
4.1.1.1. Notes from 3/5
4.2. Growth vs Decay
4.2.1. b<1 = decay and b>1 is growth
4.2.1.1. Notes from 3/5
4.3. Asymptote
4.3.1. is k and is horizontal
4.3.1.1. notes from 3/5
4.4. Transformations and Flips
4.4.1. f(x) = ab^(cx-h)+k
4.4.1.1. notes from 3/5
4.4.2. a is vertical flip
4.4.3. c is horizontal flip
4.4.4. h is left and right
4.4.5. k is up and down
5. Solving Exponents without logs
5.1. Change to common base
5.1.1. solve using exponents of bases to find x
5.1.1.1. paper notes from 3/13 & quiz of Intro to logs
5.1.1.2. same base and equal means exponents are equal