Math Problem Statement

Use the product property of logarithms to write the expression log₂(5xy) as a sum of logarithms. Assume all variables are positive.

Solution

The question asks you to rewrite the logarithmic expression log2(5xy)\log_2(5xy) using the product property of logarithms.

The product property of logarithms states:

logb(MN)=logb(M)+logb(N)\log_b(MN) = \log_b(M) + \log_b(N)

Solution:

For log2(5xy)\log_2(5xy), treat 5xy5xy as the product of three terms: 55, xx, and yy.

Using the product property:

log2(5xy)=log2(5)+log2(x)+log2(y)\log_2(5xy) = \log_2(5) + \log_2(x) + \log_2(y)

This is the simplified expression as a sum of logarithms.

Would you like further clarification or examples? Here are 5 questions to deepen your understanding:

  1. What is the product property of logarithms, and how does it simplify expressions?
  2. How do you handle logarithms with division (quotient property)?
  3. What happens when you combine logarithms with different bases?
  4. How can this rule be applied to logarithmic equations in real-world scenarios?
  5. How do logarithmic properties relate to exponents?

Tip: Always break down complex logarithmic expressions step by step using the appropriate property (product, quotient, or power).

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Math Problem Analysis

Mathematical Concepts

Logarithms
Algebra
Logarithmic Properties

Formulas

log_b(MN) = log_b(M) + log_b(N)

Theorems

Logarithmic Product Property

Suitable Grade Level

Grades 9-12