Math Problem Statement
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. one half left parenthesis log Subscript 6 Baseline a plus log Subscript 6 Baseline b right parenthesis Question content area bottom Part 1 one half left parenthesis log Subscript 6 Baseline a plus log Subscript 6 Baseline b right parenthesis
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Solution
To condense the given logarithmic expression, follow these steps:
Expression:
Step 1: Apply the Product Rule of logarithms
The product rule states: So,
Now the expression becomes:
Step 2: Apply the Power Rule of logarithms
The power rule states: Here, . So:
Step 3: Simplify
The exponent means the square root. Thus:
Final Answer:
Would you like me to explain this in more detail or assist with a related topic? Here are 5 related questions:
- How do the properties of logarithms help simplify expressions in general?
- Can you provide examples where the base of the logarithm is not 6?
- How do you evaluate logarithms with specific values, like ?
- What is the difference between condensing and expanding logarithmic expressions?
- How would this process differ if you had subtraction instead of addition inside the logarithm?
Tip: Always check for opportunities to apply logarithmic properties like the product, quotient, and power rules when simplifying expressions!
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Math Problem Analysis
Mathematical Concepts
Logarithms
Properties of Logarithms
Condensing Logarithmic Expressions
Formulas
log_b x + log_b y = log_b (x * y) (Product Rule)
c * log_b x = log_b (x^c) (Power Rule)
Theorems
Logarithm Product Rule
Logarithm Power Rule
Suitable Grade Level
Grades 10-12
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