Скачать или смотреть How to Solve Logarithmic Equations | Step-by-Step with Examples

📚 Learn How to Solve Logarithmic Equations Using Log Properties and Algebra

In this video, you’ll learn how to solve logarithmic equations by applying the properties of logarithms, rewriting them in exponential form when needed, and checking for extraneous solutions. We’ll walk through step-by-step examples that show you how to handle both types of equations—those with all terms in the same logarithmic base and those with a constant term.

These are key skills in Algebra 2 and Precalculus and essential for modeling exponential behavior in real-world applications.

🔍 What You’ll Learn in This Video:
✅ Solving Logarithmic Equations with the Same Base
✔ Use properties: product, quotient, and power rules
✔ Combine logarithms and apply the one-to-one property
✔ Example: log(x) + log(x – 1) = log(4x)
✔ Check your answers to avoid extraneous solutions

✅ Solving Logarithmic Equations with a Constant Term
✔ Combine all logarithmic terms on one side
✔ Convert to exponential form to isolate the variable
✔ Example: log₂(3x – 2) = 4
✔ Use algebra to solve and validate results

✅ Step-by-Step Examples Covered:
✔ log(x) + log(x – 1) = log(4x)
✔ 2 ln x = ln 2 + ln(3x – 4)
✔ log₃(x) + log₃(x – 3) = 1
✔ log₂(3x – 2) = 4

By the end of this lesson, you'll know when to combine logs, when to rewrite in exponential form, and how to recognize invalid solutions.

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Timestamps
00:00 Introduction
00:28 Examples - Equations with All Terms in the Same Logarithm Base
07:01 Examples - Equations with a Constant Term

More About Understand The Math
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.

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