Unit 2 Logarithmic Functions
Find exact and estimated values of logarithms.
Make conjectures about logarithm properties.
In this lesson, we found exact and approximate values for logarithmic expressions. We drew conclusions about properties of logarithms that are always true. We also identified characteristics of logarithmic functions that will help us to graph logarithms in the next lesson.
Identify common features of the graphs of logarithmic functions.
Transform the graph of a logarithmic function.
In this lesson, we graphed logarithmic functions by hand and used technology to determine common features in the graphs. We used technology to identify how the transformations appear in the equations of logarithmic functions. We examined graphs and wrote equations for the transformed functions, and we graphed transformed functions given the equations.
Use graphs to discover properties of logarithms.
Justify conjectures about logarithms.
In this lesson, we examined graphs to find equivalent expressions for logarithmic functions. We justified three logarithm properties that are true for any logarithm base. They are:
Logarithm of a Product Rule:
Logarithm of a Quotient Rule:
Logarithm of a Power Rule:
Use logarithm properties to find equivalent algebraic expressions.
Use logarithm properties to find values for logarithmic expressions using other known values.
In this lesson, we learned to find the value of a logarithmic expression combining known values and using the logarithm properties. We determined if certain logarithmic equations were true and reinforced that the logarithm product and quotient rules are only for multiplication and division inside the argument of the logarithm.
Use logarithms to solve exponential equations.
Solve systems of equations that contain exponential functions.
In this lesson, we found solutions to base
Understand how different factors affect the amount earned from compound interest.
Determine the features of a new function:
In this lesson, we explored the effects of changing the number of compounding periods in an investment that earns compound interest. In the course of this exploration, we found the number
Model continuous growth and decay using base
Solve exponential equations using natural logarithms.
In this lesson, we modeled continuous growth and decay using the formula that is a base