# 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’

accessible SL question

moderate SL / accessible HL question

discriminating SL / moderate HL question

discriminating HL question

### ♦ teaching materials

EXS_1-2-20v2_SLHL_logarithms
Exercise set for basic review of logarithms (corrected version)

EXS_1-2-25v1_HL_exponents logarithms
Exercise set for exponential & logarithmic expressions & equations

Test_SLHL_exp_log_functns_v1
Test suitable for SL and HL covering exponential and logarithmic functions (solution key below)

Test_SLHL_exp_log_functns_v1_SOL_KEY
Complete solution key for the exponential & logarithmic functions test above

Test_HL_exp_log_functions_v1
Test for HL students covering exponential and logarithmic functions (includes answers on last page)

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