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Expand the logarithm. Assume all expressions exist and are well-defined.\newlineWrite your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡(uv)\log(uv)\newline_____

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Q. Expand the logarithm. Assume all expressions exist and are well-defined.\newlineWrite your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡(uv)\log(uv)\newline_____
  1. Identify Property of Logarithm: Identify the property of logarithm used to expand log⁡(uv)\log(uv).\newlineTo expand the logarithm of a product, we use the product property of logarithms. The product property states that the logarithm of a product is equal to the sum of the logarithms of the individual factors.
  2. Apply Product Property: Apply the product property of logarithm to expand log⁡(uv)\log(uv). According to the product property: \newlinelog⁡b(PQ)=log⁡bP+log⁡bQ\log_b (PQ) = \log_b P + \log_b Q\newlineTherefore, log⁡(uv)=\log(uv) = log⁡(u)+log⁡(v)\log(u) + \log(v).

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