Math Problem Statement
Solve
Solution
To solve , we want to determine the exponent such that:
We can express 9 as . Therefore, the equation becomes:
Simplifying, we have:
Since the bases are the same, we can equate the exponents:
Solving for :
Thus, . The correct answer is .
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Related Questions:
- How do you solve logarithms with different bases?
- What is the change of base formula in logarithms?
- How do you evaluate ?
- What is the relationship between logarithms and exponents?
- How do you simplify expressions involving logarithms?
- What is the value of ?
- How do you solve logarithmic equations with multiple logarithms?
- What are common logarithms and how are they used?
Tip: Remember that logarithms can be converted to a different base using the change of base formula: .
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Math Problem Analysis
Mathematical Concepts
Logarithms
Exponents
Change of Base Formula
Formulas
\( \log_b a = \frac{\log_c a}{\log_c b} \)
Theorems
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Suitable Grade Level
Grades 10-12