Exam Strategy

Readiness Check

You are ready when you can:

• Expand and condense with product and power properties.
• Rewrite $\log_b(kx)$ and $\log_b(x^k)$ with transformation language.
• Change bases fluently.
• Recognize $\ln x=\log_e x$.

On the AP Exam

• MCQ: equivalent expressions; identify matching transformations.
• FRQ: rewrite to solve or to reveal features; justify with properties.
• Skills: 1.B equivalent forms; 3.A describe characteristics after rewriting.

Tactics

1. Expand before differentiating structure; condense before solving. 2. For $\log_b(kx)$, pull $\log_b k$ as a constant shift. 3. For $\log_b(x^k)$, bring $k$ out front as a stretch factor. 4. Change of base: $\log_b x=\log_a x/\log_a b$ (new base on both). 5. Keep arguments positive when rewriting.

Common Traps

• $\log(x+y)$ expanded as sum.
• Power on the outside vs inside.
• Upside-down change of base.
• Mixing $\ln$ and $\log_{10}$.

Quick Checklist

• [ ] Correct property named
• [ ] Equivalent form simplified
• [ ] Graph meaning if asked
• [ ] Arguments remain valid