Week 14 — Readings & Resources

Your primary reading is Chapter 14 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 71–90 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (19–23 min total)

• Tutorial 43: Logarithmic Functions — Virtual Math Lab
• Introduction to Logarithms — Mathispower4u
• Expanding Logarithmic Expressions — The Organic Chemistry Tutor

① What is a logarithm asking? The exponent question

Chapter 14, Section “Ask the exponent question” · Session 1, Segment 1, “The exponent question” · Remember: a logarithm is the exponent you need, so log₂(8) = 3 because 2³ = 8.

• Logarithms Explained — ChiliMath — a step-by-step page that switches statements between logarithmic form and exponential form, with many short conversions to check yourself against and a note on why the log of a negative number has no value; use it while working through the Week-14 module overview. (reading, 8–12 min)
• Using Logs in the Real World — BetterExplained — a friendly essay on why people measure in powers of ten, from salaries described by their number of digits to the earthquake and decibel scales, so a log becomes a count of multiplications. This builds on Week 13's work with exponential functions. (reading, 10–15 min)
• Introduction to Logarithms — Mathispower4u — the definition of a logarithm as an exponent, with conversions in both directions and several logs worked out without a calculator. (video, 8 min) (captions: creator)
• Evaluating Logarithms — Patrick J — a run of logs found in your head by asking which power of the base gives the number, including logs of fractions that come out negative. (video, 10 min) (captions: automatic)

② Where does the log graph live? Inverse, domain, and asymptote

Chapter 14, Section “Find a domain and a vertical asymptote” · Session 2, Segment 6, “Domain and vertical asymptote” · Remember: set the argument greater than zero; the boundary you find is the vertical asymptote.

• Tutorial 43: Logarithmic Functions — Virtual Math Lab — a step-by-step tutorial that defines a logarithm through its exponential form, graphs a log function as the inverse of an exponential with the x and y values switched, and finds a log function's domain by keeping the argument above zero; read the definition, the first graphing example, and the domain examples, and skip the rest. (reading, 6–10 min)
• Graphing an Exponential Function and its Inverse (a Logarithmic Function) — Mr. Allen Math — a table of points for an exponential, swapped to build its logarithm, with both curves and the mirror line drawn on one grid. (video, 5 min) (captions: automatic)
• Ex: Vertical Asymptotes and Domain of Logarithmic Functions — Mathispower4u — short examples that set the argument greater than zero, solve the inequality, and name the domain and the vertical asymptote. (video, 4 min) (captions: creator)

③ How do I split or merge logs? The three properties

Chapter 14, Section “Expand and condense: no rule for a sum” · Session 2, Segment 8, “Expand and condense” · Remember: product becomes sum, quotient becomes difference, power becomes multiplier, and a sum inside a log has no rule.

• Logarithm Rules — ChiliMath — the product, quotient, and power rules with the log of 1 and the log of the base, each followed by worked expansions. Stop here before solving logarithmic equations; next week takes that up. (reading, 8–12 min)
• Expanding Logarithmic Expressions — The Organic Chemistry Tutor — several logs of products, quotients, and powers split into simpler logs, one property at a time. (video, 5 min) (captions: automatic)
• Condensing Logarithmic Expressions — The Organic Chemistry Tutor — the reverse move: coefficients pushed up into exponents first, then the logs merged into one; pause after each example and try it first. (video, 4 min) (captions: automatic)

Optional one-stop reference (free online reference)

• Logarithm — Wolfram MathWorld — a mathematics encyclopedia's entry; read the opening definition, the notations for the common and natural logarithms, and the product, quotient, and power identities, and skip the later material on complex numbers and series, which goes beyond this course. (reading, 3–5 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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