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Expand the logarithm. Assume all expressions exist and are well-defined.\newlineWrite your answer as a sum or difference of base-66 logarithms or multiples of base-66 logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡6w6\log_6 w^6\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 base-66 logarithms or multiples of base-66 logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡6w6\log_6 w^6\newline______
  1. Identify Logarithmic Property: Identify the logarithmic property that allows expansion of log⁡6(w6)\log_6 (w^6). 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⁡6(w6)\log_6(w^6).
  2. Apply Power Property: Apply the power property to expand log⁡6(w6)\log_6(w^6). According to the power property: \newline log⁡b(mn)=n⋅log⁡b(m)\log_b(m^n) = n \cdot \log_b(m) \newline Therefore, log⁡6(w6)=6⋅log⁡6(w)\log_6(w^6) = 6 \cdot \log_6(w).

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