Math Problem Statement
Find the logarithm using the change of base formula. log Subscript 3 Baseline 19 . . . Question content area right Part 1 log Subscript 3 Baseline 19equals enter your response here (Round to four decimal places as needed.)
Solution
To find using the change of base formula, we convert it to a base-10 (or base-) logarithm. The change of base formula is:
-
Calculate and :
-
Substitute these values into the formula:
Thus:
Final Answer:
Would you like a more detailed breakdown or have any questions?
Related Questions:
- How does the change of base formula work for other logarithmic bases?
- What is the natural logarithm equivalent of ?
- How would you find using the same method?
- Why is the change of base formula useful in logarithmic calculations?
- What is the result of using base- instead of base-10?
Tip: Remember, using the change of base formula can simplify calculations when a calculator only provides (base-10) or (base-).
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Math Problem Analysis
Mathematical Concepts
Logarithms
Change of Base Formula
Formulas
Change of Base Formula: log_b(a) = log_c(a) / log_c(b)
Theorems
Properties of Logarithms
Suitable Grade Level
Grades 9-12