exponents & logarithms
► downloadable teaching materials for exponents & logarithms
► syllabus content for the Algebra Topic: SL syllabus (see syllabus section 1.2); HL syllabus (see syllabus section 1.2).
It's absolutely critical that students have a firm understanding of the relationship between exponential expressions/functions and logarithmic expressions/functions. When covering this material it is a good time to review inverse functions - and to demonstrate/explain that is the inverse of . I find it helpful to begin visually. For example, show students graphs of logarithmic functions like the one below and ask questions such as:
1. The function graphed is .
What is the value of k ?
2. State the domain and range of the function f.
3. Find the inverse of f, that is find .
4. State the domain and range of .
5. Using a GDC, find all points of intersection for and . The points of intersection lie on what line? Why?
4 questions - ‘accessible’ to ‘discriminating’
Exercise set for basic review of logarithms (corrected version)
Exercise set for exponential & logarithmic expressions & equations
Test suitable for SL and HL covering exponential and logarithmic functions (solution key below)
Complete solution key for the exponential & logarithmic functions test above
Test for HL students covering exponential and logarithmic functions (includes answers on last page)