Algebra-2

Question Analysis
This question involves finding the x-value of a point on the graph of when the y-value is -2.
The main focus is on applying the rule for logarithmic functions with negative output values, which correspond to x-values that are reciprocals of positive powers of the base.

Key Concept Explanation
For a logarithmic function , a negative y-value (e.g., y = -2) indicates that the x-value is a reciprocal of a positive power of the base. Specifically, if (where k is a positive number), then (by the negative exponent rule). Using the logarithmic property , we can find x by calculating when y = -k.

Step-by-Step Solution
Identify the base of the function : .
The given y-value is -2, so we set up the equation .
Rewrite the logarithmic equation using the negative exponent rule: If

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