AP Precalculus Review on Sections 2.9, 2.10, 2.11, and 2.12 (Reteaching and Test Practice Problems)

2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation

1. Converting logarithmic functions to exponential functions and vice versa: This involves understanding the relationship between logarithmic and exponential expressions and being able to switch between them. For example, if you have a logarithmic equation like log(base b) of x = y, you can convert it to an exponential form as b^y = x.

2. Solving logarithmic and exponential functions: This includes solving equations involving logarithmic and exponential expressions. You use properties and rules of these functions to find unknown values.

3. The change of base formula: This formula allows you to change the base of a logarithm. It's typically used when you want to evaluate a logarithm with a base different from common bases like 10 or e.

4. Exponential regression on the TI-84+: This involves using a graphing calculator, such as the TI-84+, to perform exponential regression analysis on data points. It helps find the best-fitting exponential model for a set of data.

5. Graphing exponential and logarithmic functions: This covers the process of plotting and understanding the graphs of exponential and logarithmic functions, including their key characteristics like asymptotes, growth/decay, and intercepts.

6. Finding and comparing the graphs of inverses of logarithmic and exponential functions: This involves understanding the concept of function inverses and how to find and compare the graphs of the inverses of logarithmic and exponential functions.

7. Word problems involving logarithms: In real-world scenarios, logarithms are used to solve problems related to exponential growth, decay, or other processes. Word problems require translating the situation into mathematical equations involving logarithmic functions.

8. Continuously compounded interest: This relates to finance and compound interest. It involves understanding the formula A = P * e^(rt), where A is the final amount, P is the principal, r is the annual interest rate, t is the time in years, and e is the mathematical constant approximately equal to 2.71828. Continuous compounding is used in situations where interest is continuously added to the principal.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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[ishab]

47:30
how is 2e^{x}=7 the same as e^{2x}=7
?
is there a rule I'm missing or something?

[shripadsg]

Many thanks!
I can not see UNIT 3?
Can u help?