Calculations with logarithms
A:
- Definition of logarithm
- Domains of logarithmic expressions
B:
- Logarithms counting rules
C:
- Simplifying expressions with logarithms of various base
Exponential functions
A:
- Definition of the exponential function
- Graph and its transformations
- Domain and range
B:
- Exponential function properties – monotonicity, boundedness
- Comparing of function values (with aid of graphs or monotonicity)
C:
- Composite functions (with absolute values or radicals)
- Practical word problems
Logarithmic functions
A:
- Definition of the logarithmic function
- Graph and its transformations
- Domain and range
B:
- Logarithmic function properties – monotonicity, boundedness
- Comparing of function values (with aid of graphs or monotonicity)
C:
- Composite functions (with absolute values or radicals)
- Practical word problems
Exponential equations and inequalities
A:
- Equations with the same base - solvable by comparing exponents
B:
- Equations with the same base (more complex) - solvable by comparing exponents
- Equations solvable by substitution
C:
- Inequalities solvable by comparing exponents
- Inequalities solvable by substitution
- System of inequalities
Logarithmic equations and inequalities
A:
- 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
B:
- 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
C:
- Inequalities solvable by simplifying and comparing arguments
- Inequalities solvable by substitution
