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Condense the logarithm 5log d+log x Answer: log(◻)

Condense the logarithm\newline5log⁡d+log⁡x 5 \log d+\log x \newlineAnswer: log⁡(□) \log (\square)

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Q. Condense the logarithm\newline5log⁡d+log⁡x 5 \log d+\log x \newlineAnswer: log⁡(□) \log (\square)
  1. Apply Power Rule: Apply the power rule of logarithms to the term 5log⁡d5\log d. The power rule states that alog⁡b(c)=log⁡b(ca)a\log_b(c) = \log_b(c^a). Therefore, we can rewrite 5log⁡d5\log d as log⁡(d5)\log(d^5). Calculation: 5log⁡d=log⁡(d5)5\log d = \log(d^5)
  2. Combine Logarithmic Terms: Combine the two logarithmic terms using the product rule.\newlineThe product rule of logarithms states that log⁡b(m)+log⁡b(n)=log⁡b(m∗n)\log_b(m) + \log_b(n) = \log_b(m*n). Therefore, we can combine log⁡(d5)\log(d^5) and log⁡x\log x into a single logarithm.\newlineCalculation: log⁡(d5)+log⁡x=log⁡(d5∗x)\log(d^5) + \log x = \log(d^5 * x)
  3. Write Final Answer: Write the final answer.\newlineThe expression 5log⁡d+log⁡x5\log d + \log x has been condensed into log⁡(d5×x)\log(d^5 \times x).

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