Math Problem Statement
Solution
To rewrite the given logarithmic expression using properties of logarithms, let’s go step by step.
We are asked to rewrite: using logarithmic properties.
Step 1: Apply the logarithm to the product
By the product property of logarithms, , we can split the logarithm of a product:
Step 2: Apply the logarithm to the fraction
Now, use the quotient property of logarithms, , on :
Step 3: Combine the results
Now, combine both steps:
Final expression:
Correct answer:
The correct answer matches the second option:
Would you like any further clarifications or details on logarithmic properties?
Here are 5 additional related questions:
- What is the logarithmic property used for powers of variables?
- How does the logarithmic product property differ from the quotient property?
- How would you handle the expression if had a different base?
- Can you rewrite without expanding the logarithm?
- How do logarithmic properties help simplify complex expressions?
Tip: Always remember that logarithms turn multiplication into addition and division into subtraction, which helps simplify complex products and quotients.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Algebra
Formulas
Product property of logarithms: log_b(xy) = log_b(x) + log_b(y)
Quotient property of logarithms: log_b(x/y) = log_b(x) - log_b(y)
Power rule of logarithms: log_b(x^n) = n * log_b(x)
Theorems
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Suitable Grade Level
Grades 9-12