Question #6451907Fill in the Blank
Algebra-2
Question
The graph of passes through the point ______.
Answer & Analysis
Analysis
Question Analysis
This question involves finding the x-value of a key point on the graph of when the y-value is -1.
The main focus is on using the relationship between logarithms and negative exponents to solve for .
Key Concept Explanation
For a logarithmic function :
When , this means . Using the definition of logarithms, this converts to the exponential form .
A negative exponent rule tells us (e.g., ). Thus, when , the x-value is .
Step-by-Step Solution
Set the function equal to -1: .
Convert to exponential form using : Here,
This question involves finding the x-value of a key point on the graph of when the y-value is -1.
The main focus is on using the relationship between logarithms and negative exponents to solve for .
Key Concept Explanation
For a logarithmic function :
When , this means . Using the definition of logarithms, this converts to the exponential form .
A negative exponent rule tells us (e.g., ). Thus, when , the x-value is .
Step-by-Step Solution
Set the function equal to -1: .
Convert to exponential form using : Here,
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