Identify Properties Of Logarithms Given Equation Worksheets [PDF]: Algebra 2 Math

How Will This Worksheet on "Identify Properties of Logarithms Given Equation" Benefit Your Student's Learning?

Understanding logarithmic properties allows students to simplify tough equations faster, which is crucial during exams and assignments.
Mastery of logarithmic relationships helps students grasp concepts more intuitively, making problem-solving easier and more effective.
Knowing logarithmic properties well sets a strong base for tackling higher-level math subjects like calculus and advanced algebra.
Applying logarithmic rules enhances analytical thinking and logical reasoning, which are vital for solving complex problems in various subjects.

First, identify if the equation follows logarithmic rules such as the product, quotient, or power rules.
Confirm the base `b` used in all logarithmic terms within the equation.
Then, combine the logarithmic terms using the identified properties to reduce the equation to its simplest logarithmic expression.
Confirm that the simplified expression on the left side matches the right side.
Simplify the logarithmic expression further if possible, ensuring clarity and correctness in the equation.

Solved Example

Q. Which property of logarithms does this equation demonstrate?

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\log_3 3 + \log_3 6 = \log_3 18

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Choices:

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(A)

\text{Product Property}

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(B)

\text{Power Property}

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(C)

\text{Quotient Property}

Solution:

Analyze the equation: Analyze the given equation. $\newline$ We have the equation $\log_3 3 + \log_3 6 = \log_3 18$ . We need to determine which logarithmic property this equation represents.
Recall logarithmic properties: Recall the properties of logarithms. $\newline$ There are three main properties of logarithms that are relevant to this problem: the Product Property, the Power Property, and the Quotient Property. The Product Property states that $\log_b (P) + \log_b (Q) = \log_b (PQ)$ , the Power Property states that $n \cdot \log_b (P) = \log_b (P^n)$ , and the Quotient Property states that $\log_b (P) - \log_b (Q) = \log_b \left(\frac{P}{Q}\right)$ .
Match equation with property: Match the given equation with the correct property. $\newline$ The given equation is $\log_3 3 + \log_3 6 = \log_3 18$ . This matches the form of the Product Property, which states that the sum of the logarithms is equal to the logarithm of the product of the bases: $\log_b (P) + \log_b (Q) = \log_b (PQ)$ .
Verify equation using property: Verify the equation using the Product Property. $\newline$ Using the Product Property, we can combine the logarithms on the left side of the equation: $\log_3 (3 \times 6) = \log_3 18$ . Since $3 \times 6$ equals $18$ , the equation is correct and demonstrates the Product Property.