Math Problem Statement
Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. log Subscript b Baseline left parenthesis z cubed y right parenthesis Question content area bottom Part 1 log Subscript b Baseline left parenthesis z cubed y right parenthesis equals 3. log Subscript b Baseline left parenthesis z right parenthesis plus log Subscript b Baseline left parenthesis y right parenthesis
Solution
To expand using the properties of logarithms, follow these steps:
Step 1: Apply the product rule of logarithms
The product rule states: Applying this rule:
Step 2: Apply the power rule of logarithms
The power rule states: Using this rule on :
Step 3: Combine the terms
Substitute back into the expression:
Final Answer:
If there are any specific values for or , you can substitute them in to evaluate further.
Would you like additional examples or clarifications?
Related Questions:
- How do the product and power rules of logarithms differ?
- Can you simplify using logarithmic rules?
- What happens if one of the terms is zero or undefined in a logarithmic expression?
- How do these rules apply to natural logarithms ()?
- How do you solve for if and are known?
Tip:
Always check the domain of the variables in logarithmic expressions. For example, and are required for to be defined.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Properties of Logarithms
Algebra
Formulas
Product rule: log_b(xy) = log_b(x) + log_b(y)
Power rule: log_b(x^n) = n * log_b(x)
Theorems
Properties of Logarithms
Suitable Grade Level
Grades 9-11