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Math  /  Algebra

QuestionChoose the expression that shows an expanded form of the logarithm. ln⁡(x10x−13x−20)(12)ln⁡x10(x−1)−ln⁡(3x−20)10ln⁡x+(12)ln⁡(x−1)−ln⁡(3x−20)10ln⁡x+ln⁡x−1−ln⁡(3x−12)\begin{array}{c} \ln \left(\frac{x^{10} \sqrt{x-1}}{3 x-20}\right) \\ \left(\frac{1}{2}\right) \ln x^{10}(x-1)-\ln (3 x-20) \\ 10 \ln x+\left(\frac{1}{2}\right) \ln (x-1)-\ln (3 x-20) \\ 10 \ln x+\ln \sqrt{x-1}-\ln (3 x-12) \end{array}

Studdy Solution
Combine the results from the previous steps:
ln⁡(x10x−13x−20)=10ln⁡x+12ln⁡(x−1)−ln⁡(3x−20)\ln \left(\frac{x^{10} \sqrt{x-1}}{3x-20}\right) = 10 \ln x + \frac{1}{2} \ln(x-1) - \ln(3x-20)
The expanded form of the logarithm is:
10ln⁡x+12ln⁡(x−1)−ln⁡(3x−20)10 \ln x + \frac{1}{2} \ln(x-1) - \ln(3x-20)

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