Question #6452357Fill 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 product rule and converting them into exponential form.
This problem assesses the ability to solve logarithmic equations using the product rule and converting them into exponential form.
Key Concept Explanation
The product rule for logarithms states that . In this case, can be rewritten as .
The product rule for logarithms states that . In this case, can be rewritten as .
Step-by-step Solution
1. Combine the logarithms using the product rule:
2. Simplify the argument:
3. Convert the logarithmic equation to exponential form:
4. Simplify the exponential term:
5. Rearrange the equation:
1. Combine the logarithms using the product rule:
2. Simplify the argument:
3. Convert the logarithmic equation to exponential form:
4. Simplify the exponential term:
5. Rearrange the equation:
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