Common Mistakes

Frequent Errors

1. Saying $\log_b c = b/c$ or $c/b$. 2. Evaluating logs of zero or negatives as real numbers. 3. Using base $b=1$ or $b\le 0$. 4. Forgetting unspecified $\log$ is base 10. 5. Confusing $\log_b(b^k)$ with $b^k$. 6. Reading a log scale as if gaps were additive differences. 7. Claiming $\log_b 1 = 1$ instead of 0. 8. Estimating without bounding between known powers.

Why These Happen

Students import fraction language onto logs and treat scale labels like ordinary number lines.

How to Fix Them

• Mandatory exponential rewrite for every evaluation.
• Validity checklist: $b>0$, $b\neq 1$, $c>0$.
• Power tables for common bases.
• Say: "each log tick multiplies."

Avoidance Scripts

• "$\log_b c$ is the exponent on $b$ that makes $c$."
• "$\log_b 1=0$ because $b^0=1$."
• "Between $10^1$ and $10^2$ means between 1 and 2 for $\log_{10}$."

Quick Self-Check

• Did I convert to exponential form?
• Are base and argument valid?
• Exact power or technology estimate?