Week 15 · Readings & resources

Week 15 — Readings & Resources

College Algebra Free sample edition

Your primary reading is Chapter 15 (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 66–82 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 (20–24 min total)

① How do I get x out of the exponent? Match the bases or take a log

Chapter 15, Section “Take a logarithm of both sides” · Session 1, Segment 3, “Take a logarithm of both sides” · Remember: match the bases when you can; when you cannot, take the same log of both sides and bring the exponent down.

Exponential Functions — Math Hints — the section on solving by matching bases, near the end of the page, rewrites both sides as powers of the smallest shared base, such as 9 and 27 as powers of 3, sets the exponents equal, and checks each answer; skip the graphing-calculator steps. Use it while working through the Week-15 module overview. (reading, 8–12 min)
Solving Exponential Equations Using Logarithms — ChiliMath — examples where no common base exists, so a logarithm of both sides brings the exponent down; notice that either log gives the same value as long as both sides get the same one. This builds on Week 14's work with the properties of logarithms. (reading, 6–10 min)
Solving Exponential Equations with the Same Bases — MyMathEducation — three short examples: bases that already match, bases that can be made to match, and a base hidden behind a negative exponent; set the exponents equal and solve what is left. (video, 7 min) (captions: automatic)
Ex 4: Solve Exponential Equations Using Logarithms — Mathispower4u — two equations solved by isolating the power, taking a log of both sides, and giving the exact answer before the decimal. (video, 5 min) (captions: creator)

② Which answers survive? Logarithmic equations and the domain check

Chapter 15, Section “Condense, convert, and run the domain check” · Session 1, Segment 5, “Condense, convert, and check” · Remember: condense to one log, convert to a power, and reject any candidate that puts a zero or a negative inside a log.

Extraneous Solutions: Causes and Cures — The Math Doctors — a long-running math help service explains why correct-looking steps can create answers that fail the original equation, with logs, roots, and fractions as the usual causes, and when a check is truly required. (reading, 12–16 min)
Solving Logarithmic Equations (5 Examples) — Mario's Math Tutoring — five equations solved by condensing, converting to exponential form, and checking; pause before each check and do it yourself. (video, 11 min) (captions: automatic)
Solving Logarithmic Equations, Example 1 — Patrick J — one equation where combining two logs leads to a quadratic, so both factored candidates have to be tested against the logs they came from. (video, 3 min) (captions: automatic)

③ How long until it doubles or halves? Growth and decay times

Chapter 15, Section “Find a doubling time” · Session 2, Segment 6, “Doubling time” · Remember: divide away the starting amount, take ln of both sides, and the time depends only on the rate.

Radionuclides — U.S. Environmental Protection Agency — a short government page on why each radioactive material is described by its own half-life, from seconds to millions of years; read the opening section and skip the list of individual materials. (reading, 3–5 min)
Time to Double Compounding Continuously — Mario's Math Tutoring — a continuous-compounding balance set equal to twice its start, then solved for the time with natural logs. (video, 2 min) (captions: automatic)
Exponential Decay App with Logs: Find Half Life — Mathispower4u — builds a decay model of the form A = A₀ · e^(kt) from given data, with a negative k, and then solves for the time when half remains. (video, 7 min) (captions: creator)

Optional one-stop reference (free online reference)

Half-Life — Wolfram MathWorld — a mathematics encyclopedia's short entry; read the definition and the formula that ties the half-life to the decay constant, and skip the remark on the characteristic decay time, which goes beyond this course. (reading, 2–4 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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