Exponentials and Logarithms

The topic is divided into the following subtopics:

Calculations with Logarithms
Exponential Functions
Logarithmic Functions
Exponential Equations and Inequalities
Logarithmic Equations and Inequalities

Calculations with Logarithms

Part I:

Definition of logarithm
Domains of logarithmic expressions

Part II:

Logarithms counting rules

Part III:

Simplifying expressions with logarithms of various base

Exponential Functions

Part I:

Definition of the exponential function
Graph and its transformations
Domain and range

Part II:

Exponential function properties – monotonicity, boundedness
Comparing of function values (with aid of graphs or monotonicity)

Part III:

Composite functions (with absolute values or radicals)
Practical word problems

Logarithmic Functions

Part I:

Definition of the logarithmic function
Graph and its transformations
Domain and range

Part II:

Logarithmic function properties – monotonicity, boundedness
Comparing of function values (with aid of graphs or monotonicity)

Part III:

Composite functions (with absolute values or radicals)
Practical word problems

Exponential Equations and Inequalities

Part I:

Equations with the same base - solvable by comparing exponents

Part II:

Equations with the same base (more complex) - solvable by comparing exponents
Equations solvable by substitution

Part III:

Inequalities solvable by comparing exponents
Inequalities solvable by substitution
System of inequalities

Logarithmic Equations and Inequalities

Part I:

Equations with the logarithms of the same base - solvable by comparing arguments
Equations with the logarithms of the same base – solvable with use of logarithm counting rules

Part II:

Equations with the logarithms of the same base (more complex) – solvable with use of logarithm counting rules
Equations with logarithms of various bases
Equations solvable by substitution
Equations solvable by taking logarithm
System of equations

Part III:

Inequalities solvable by simplifying and comparing arguments
Inequalities solvable by substitution