Identify Properties Of Logarithms Given Equation Worksheet

Algebra 2
Logarithms

Total questions - 0

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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.

How to Identify Properties of Logarithms Given Equation?

  • 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? \newlinelog33+log36=log318\log_3 3 + \log_3 6 = \log_3 18\newlineChoices:\newline(A) Product Property\text{Product Property}\newline(B) Power Property\text{Power Property}\newline(C) Quotient Property\text{Quotient Property}
Solution:
  1. Analyze the equation: Analyze the given equation.\newlineWe have the equation log33+log36=log318\log_3 3 + \log_3 6 = \log_3 18. We need to determine which logarithmic property this equation represents.
  2. Recall logarithmic properties: Recall the properties of logarithms.\newlineThere 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 logb(P)+logb(Q)=logb(PQ)\log_b (P) + \log_b (Q) = \log_b (PQ), the Power Property states that nlogb(P)=logb(Pn)n \cdot \log_b (P) = \log_b (P^n), and the Quotient Property states that logb(P)logb(Q)=logb(PQ)\log_b (P) - \log_b (Q) = \log_b \left(\frac{P}{Q}\right).
  3. Match equation with property: Match the given equation with the correct property.\newlineThe given equation is log33+log36=log318\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: logb(P)+logb(Q)=logb(PQ)\log_b (P) + \log_b (Q) = \log_b (PQ).
  4. Verify equation using property: Verify the equation using the Product Property.\newlineUsing the Product Property, we can combine the logarithms on the left side of the equation: log3(3×6)=log318\log_3 (3 \times 6) = \log_3 18. Since 3×63 \times 6 equals 1818, the equation is correct and demonstrates the Product Property.
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About Worksheet

Algebra 2
Logarithms

To identify properties of logarithms given an equation, look for ways to apply logarithmic rules such as the product rule \(\log_b(xy) = \log_b(x) + \log_b(y)\), the quotient rule `\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)`, and the power rule \(\log_b(x^k) = k \log_b(x)\). Recognizing these properties allows us to simplify and solve logarithmic equations more effectively.  

Example: Given the equation \(\log_b(x^2) = 2 \log_b(x)\), identify the logarithmic property used.

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