Math Problem Statement
Use common logarithms or natural logarithms and a calculator to evaluate the expression. log Subscript 14 Baseline 17 Question content area bottom Part 1 Evaluate the expression. log Subscript 14 Baseline 17almost equals enter your response here (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed.)
Solution
To evaluate using common logarithms () or natural logarithms (), we can apply the change of base formula:
Step 1: Apply the formula
Step 2: Calculate using a calculator
Final Answer:
Would you like a detailed explanation of the change of base formula?
Here are 5 related questions to expand on this topic:
- How do you convert between natural logarithms and common logarithms?
- Why is the change of base formula valid for all logarithms?
- How can you use logarithms to solve exponential equations?
- What is the difference between natural and common logarithms in applications?
- How do logarithmic properties simplify complex expressions?
Tip: Always carry extra decimal places in intermediate steps to reduce rounding errors, then round only the final answer.
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Math Problem Analysis
Mathematical Concepts
Logarithms
Change of Base Formula
Formulas
\log_b{a} = \frac{\log{a}}{\log{b}}
\log_b{a} = \frac{\ln{a}}{\ln{b}}
Theorems
Change of Base Formula
Suitable Grade Level
Grades 9-12