# Exponents 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