Solve the logarithmic equation: .

Answer and explanation

Correct answer: B.

  1. Step 1: Combine the logarithms using the product law : . Converting from logarithmic to exponential form gives .
  2. Step 2: Expand and solve the quadratic: , giving or . Since logarithms are defined only for strictly positive arguments, , rejecting as extraneous. Thus .
Answer
.
Why not the others: The value produces undefined logarithms of negative numbers ; retaining both and fails to discard the extraneous root; evaluates to .

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