Question #6452369Fill 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, specifically the quotient rule.
This problem assesses the ability to solve logarithmic equations using the properties of logarithms, specifically the quotient rule.
Key Concept Explanation
The quotient rule states that . We can use this to combine the logarithms and then convert the equation to its exponential form.
The quotient rule states that . We can use this to combine the logarithms and then convert the equation to its exponential form.
Step-by-step Solution
1. Combine the logarithms using the quotient rule: .
2. Convert to exponential form: .
3. Solve the resulting rational equation: ( ).
4. Expand and simplify:
1. Combine the logarithms using the quotient rule: .
2. Convert to exponential form: .
3. Solve the resulting rational equation: ( ).
4. Expand and simplify:
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