1. Algebra 2/Trigonometry Name: __________________________
Section 8.4 – Logarithms Notes Date: ___________________________
Recall: To find an inverse of a function, _______________________________________. Create a table of values for y = 2x. Use the table of values to graph y and its inverse. x y x y
This inverse is called a ____________________________________________________ ______________________________________________________________________
Definition of Logarithmic Function with Base a–
For x > 0, a > 0, and a ¹ 1,
Graphing Logarithmic Functions
Characteristics:
Shifting Graphs of Logarithmic Functions

2. __________________________________________
Converting Logarithms to Exponentials
Ex.1: Ex.2: Ex.3: Ex.4:
Converting Exponentials to Logarithms
Ex.1: Ex.2: Ex.3: Ex.4:
The logarithmic function _________________________________________ ________________________________________________________________________________________________________________________
__________________________________________
____________________________________________________________
Evaluating Common Logarithms. Given f(x) = logx, find:
Example 1:
Example 2:
Example 3:
Evaluating Logarithms (other than base 10)
Example 1:
Example 3:
Example 2:
Example 4:

3. Algebra 2/Trigonometry Section 8.4 – Logarithms Notes – Day 1
Properties of Logarithms:
1) ____________________________________________________________________
2) ____________________________________________________________________
3) ____________________________________________________________________
4) ____________________________________________________________________
Using Properties of Logarithms:
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Example 6:

4. Algebra 2/Trigonometry
Section Natural Base & Natural Logarithms Notes – Day 2
The Natural Base, e – In many applications, the natural base, e, is used.
e » … is an ____________________________________________.
The function given by f(x) = ex is called the ____________________________________. e is the constant term and x is the variable.
Evaluating the Natural Exponential Function:
Graph of the Natural Exponential Function:
The Natural Logarithmic Function –
Evaluating the Natural Logarithmic Function:
Properties of Natural Logarithms:
1) ____________________________________________________________________
2) ____________________________________________________________________
3) ____________________________________________________________________
4) ____________________________________________________________________

5. Using Properties of Natural Logarithms:
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Example 6:
Example 7:
Compounding Interest Continued x 1 10
100
1,000
10,000
100,000
1,000,000 
What if the interest compounded continuously?
Compounded Continuously
Interest Formula
Example - A total of $12,000 is invested at an annual interest rate of 9%. Find the balance after 5 years if it is compounded…
quarterly.
(b) monthly.
(c) continuously.

6. Population Growth/Decay P = Population C = Initial value
k = rate of growth/decay
t = number of years
The population of a small town continuously grows at a rate of 0.5%. If the population is currently about 4,300 people ...
Write an equation that models the situation
b) Predict the population next year
c) Predict the population 10 years from now
Example - You purchase a car for $40,000, and it depreciates in value at a rate of 11%.
a) Write an equation to represent the situation.
b) Find the approximate value of your car after 8 years.
Class work: Working with your partner, complete the table (on a separate piece of paper) using the given problem situation. Show all work and round any answers to the nearest hundredth (nearest cent). You will be turning this in!! You are adding compounding continuously. If you made any mistakes for your last submission, please fix them for this one!
Compounded
Interest Earned
Value of Account
Annually
Monthly
Weekly
Daily
Hourly
Continuously
Imagine you were given $10,000 for graduation from high school. If you invested that amount into an account that yields an APR of 4.5% and left the money in your investment for the next 10 years, how much money would you have? How much interest would you accrue?