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Common Mistakes

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Frequent Errors

1. $\log_b(x+y)=\log_b x+\log_b y$ (false). 2. $\log_b(x^n)=(\log_b x)^n$ (false). 3. $\log_b(x/y)=\log_b x/\log_b y$ (false). 4. Change of base upside down: $\log_a b/\log_a x$. 5. Dropping the $\log_b k$ meaning when rewriting $\log_b(kx)$. 6. Treating $\ln$ as common log. 7. Ignoring domain ($x>0$, and factors positive as required). 8. Condensing with incorrect coefficients.

Why These Happen

Students import fraction/distribution habits onto logs and mix transformation language.

How to Fix Them

Property flashcards with one counterexample each.
Always rewrite with exponential meaning as a check.
For change of base, say: "same new base top and bottom."

Avoidance Scripts

"Products become sums; powers become multipliers."
"Cannot distribute log over addition."
"$\ln$ means base $e$."

Quick Self-Check

Did I use product/power correctly?
Is change of base oriented right?
Does my rewrite match a known graph move?

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