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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⁡v7\log v^7 \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⁡v7\log v^7 \newline______
  1. Identify Logarithmic Property: Identify the logarithmic property that allows expansion of log⁡(v7)\log(v^7). To expand the logarithm of power, we use the power property of logarithms. \newlineThe power property of logarithms states that log⁡b(mn)=n⋅log⁡b(m)\log_b(m^n) = n \cdot \log_b(m), which can be used to expand log⁡(v7)\log(v^7).
  2. Apply Power Property: Apply the power property to expand log⁡(v7)\log(v^7). According to the power property: \newline log⁡b(mn)=n⋅log⁡b(m)\log_b(m^n) = n \cdot \log_b(m) \newlineTherefore, log⁡(v7)=7⋅log⁡(v)\log(v^7) = 7 \cdot \log(v).

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