Common Mistakes
Pre-calculus · AP · Exponential and Logarithmic Functions
Focus
Inverses of Exponential Functions
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. Log property misuse
What it looks/sounds like: Logs of sums/products are ‘split’ incorrectly.
Why it happens: Log rules are memorized without structure.
How to fix: Rewrite as a single log before applying properties; check domain.
### 2. Growth/decay misread
What it looks/sounds like: Base between 0 and 1 is treated as growth.
Why it happens: The base is not compared to 1.
How to fix: Ask: is the base > 1 (growth) or 0 < base < 1 (decay)?
### 3. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 4. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. Translate between exponential and log forms before solving. 2. Interpret parameters in context with units. 3. Check log arguments are positive.
Quick self-check
- [ ] Can identify growth vs decay from an equation
- [ ] Can fix a log-domain error
- [ ] Can interpret a parameter in words