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Expand the logarithm. Assume all expressions exist and are well-defined. Write 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. log⁡uv \log uv

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Properties of logarithms: mixed reviewright chevron icon

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Q. Expand the logarithm. Assume all expressions exist and are well-defined. Write 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. log⁡uv \log uv
  1. Identify Property: Identify the property of logarithm used to expand log⁡uv\log uv. Product property is used to expand a product within a logarithm.
  2. Apply Property: Apply the product property to expand log⁡uv\log uv. Product Property: log⁡b(PQ)=log⁡bP+log⁡bQ\log_b (PQ) = \log_b P + \log_b Q\newline log⁡uv=log⁡(u)+log⁡(v)\log uv = \log(u) + \log(v)

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