Question #6452358Fill in the Blank
Algebra-2
Question
Solve the equation . The value of is ________.
Answer & Analysis
Analysis
Question Analysis
This problem assesses the ability to solve logarithmic equations using the properties of logarithms and the one-to-one property.
This problem assesses the ability to solve logarithmic equations using the properties of logarithms and the one-to-one property.
Key Concept Explanation
The quotient rule for logarithms states that . The one-to-one property states that if , then .
The quotient rule for logarithms states that . The one-to-one property states that if , then .
Step-by-step Solution
1. Combine the logarithms using the quotient rule: .
2. Convert the logarithmic equation to its exponential form: .
3. Solve the resulting rational equation: ( ).
4. Expand and simplify:
1. Combine the logarithms using the quotient rule: .
2. Convert the logarithmic equation to its exponential form: .
3. Solve the resulting rational equation: ( ).
4. Expand and simplify:
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