Study Guide

Learning Objectives

• Translate between $\log_b c = a$ and $b^a = c$ (2.9.A.1).
• Evaluate exact logarithmic expressions using known powers (2.9.A.2).
• Estimate other log values with technology when needed (2.9.A.2).
• Interpret units on a logarithmic scale as multiplicative base changes (2.9.A.3).
• Recognize that unspecified $\log$ means base 10 (2.9.A.1).

Suggested Practice Sequence

1. Convert $\log_b c = a$ $\leftrightarrow$ $b^a = c$. 2. Exact: $\log_2 16$, $\log_3 27$, $\log_{10} 1000$, $\log_5 1$. 3. Special values: $\log_b 1=0$, $\log_b b=1$, $\log_b(b^k)=k$. 4. Estimate $\log_{10} 50$ between 1 and 2; refine with calculator. 5. Read a log-scale axis: each tick multiplies by 10 (or base $b$).

Classroom / Check-In Moves

• "Say the exponential" after every log answer.
• Power-bank card sort for bases 2, 3, 5, 10.
• Linear vs log number-line comparison.

Misconception Watch-List

• $\log_b(c)=c^b$ or $b/c$.
• $\log(-4)$ as a real number.
• Base 1 or negative base.
• Confusing $\log$ (base 10) with $\ln$ (base $e$).

Vocabulary to Own

• logarithm; base; argument
• common logarithm ($\log_{10}$)
• exact value; estimate; technology
• logarithmic scale; multiplicative change

Materials Map

• Practice: evaluate and convert forms
• Word: pH, Richter, decibel-style scales
• Mixed / multi-*: link to exponentials (2.3–2.5) and inverses (2.8)
• Review & practice test: timed log fluency
• Interactive: meaning and evaluation checks