QuestionUse properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. $\ln \left[\frac{x^{5} \sqrt{x^{2}+5}}{(x+5)^{4}}\right]$ $\ln \left[\frac{x^{5} \sqrt{x^{2}+5}}{(x+5)^{4}}\right]=$

Studdy Solution
Combine all the expanded parts together:
$\ln \left[\frac{x^{5} \sqrt{x^{2}+5}}{(x+5)^{4}}\right] = 5 \ln x + \frac{1}{2} \ln (x^{2}+5) - 4 \ln (x+5)$
This is the expanded form of the logarithmic expression.

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