Question #6452355Fill 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 quotient rule and converting them into exponential form.
This problem assesses the ability to solve logarithmic equations using the quotient rule and converting them into exponential form.
Key Concept Explanation
The quotient rule for logarithms states that . In this case, can be rewritten as .
The quotient rule for logarithms states that . In this case, can be rewritten as .
Step-by-step Solution
1. Combine the logarithms using the quotient rule:
2. Convert the logarithmic equation to exponential form:
3. Solve the rational equation: Multiply both sides by : ( )
4. Expand and simplify:
1. Combine the logarithms using the quotient rule:
2. Convert the logarithmic equation to exponential form:
3. Solve the rational equation: Multiply both sides by : ( )
4. Expand and simplify:
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