Question #6452362Fill in the Blank
Algebra-2
Question
Solve the equation . The value of is ________.
Answer & Analysis
Analysis
Question Analysis
This problem tests the ability to use the properties of logarithms to combine and solve logarithmic equations.
This problem tests the ability to use the properties of logarithms to combine and solve logarithmic equations.
Key Concept Explanation
The key concept is the use of the quotient rule of logarithms, which states that . After combining the logarithms, the equation can be converted to exponential form.
The key concept is the use of the quotient rule of logarithms, which states that . After combining the logarithms, the equation can be converted to exponential form.
Step-by-step Solution
1. Combine the logarithms using the quotient rule: .
2. Convert the logarithmic equation to its exponential form: .
3. Simplify the exponential form: .
4. Solve the rational equation: Multiply both sides by (note , so ):
1. Combine the logarithms using the quotient rule: .
2. Convert the logarithmic equation to its exponential form: .
3. Simplify the exponential form: .
4. Solve the rational equation: Multiply both sides by (note , so ):
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