Math Problem Statement
log 7 (15) to base e
Solution
To convert the logarithm to base , we use the change of base formula for logarithms:
Here, and . So:
Now, using approximate values for the natural logarithms:
Thus, to base is approximately 1.391.
Would you like further details or have any questions?
Here are some related questions you might find interesting:
- What is the change of base formula for logarithms?
- How do you derive the natural logarithm () of a number?
- Can you calculate to base ?
- What is the significance of natural logarithms in mathematics?
- How can logarithmic identities simplify complex logarithmic expressions?
Tip: The change of base formula is very useful when you need to compute logarithms with a calculator that only supports base 10 or base .
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Math Problem Analysis
Mathematical Concepts
Logarithms
Change of Base Formula
Natural Logarithms
Formulas
log_b(a) = ln(a) / ln(b)
Theorems
Change of Base Theorem
Suitable Grade Level
Grades 10-12
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