Math Problem Statement
Evaluate. log Subscript 3 Baseline StartFraction 1 Over 243 EndFraction Question content area bottom Part 1 log Subscript 3 Baseline StartFraction 1 Over 243 EndFraction equals enter your response here
Solution
To evaluate , let's proceed step by step:
Step 1: Express as a power of 3.
We know that . Therefore:
Step 2: Use the logarithmic property.
We apply the logarithmic rule . In this case:
Step 3: Simplify using .
Thus:
Final answer:
Would you like further details or explanations?
Here are 5 related questions:
- What is ?
- How do you simplify for any base ?
- What is ?
- Can you explain the change of base formula for logarithms?
- How do logarithms behave when the base is a fraction?
Tip: When evaluating logarithms of fractions, express the fraction in terms of a power of the base to simplify.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Algebra
Formulas
log_b (a^c) = c * log_b (a)
log_b (b) = 1
Theorems
Logarithmic Properties
Suitable Grade Level
Grades 9-11