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In this comprehensive guide to solving logarithmic equations, we focus on the key principles of logarithms and their properties. We emphasize the importance of like bases and the equality of exponents. Key methods, including the Quadratic Formula and factoring, are presented alongside practical examples. We'll demonstrate why direct operations on logs can lead to errors, stressing the importance of applying logarithmic properties properly. This first part serves as a foundation for more complex equations, preparing you for further challenges in the realm of logarithms.
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Solving Logarithmic Equations PART ONE
Recall: If we have like bases then the exponents are equal. Use Quadratic Formula or Factor or P/Q. 0 = (x - 4)(x + 1)
YOU CANNOT DIVIDE 14 by 2 NOR CAN YOU CANCEL OUT THE LOGS!!! Take the log of both sides so that we can use the PROPERTIES!!! Remember that log 2 is just a number so divided both sides by log 2. Divide by 3 first. log log log 2 log 2 = 3.807
Move 4 and divide by 2. Let’s take a logof each side. log log Now that we’ve take the log of each side we can use are properties. log 3 log 3
Move 4. ln ln Because we have an “e” we use natural logs. Remember that the ln e is ONE!!!
Use QF or factor Set each factor equal to zero and solve using natural logs.
