1 Answer

HubballiHuli · Answer 1 · 2023-05-21T11:24:37+0000

Answer:
$\ln ((x+2))/(x^4(x^2+6))$ Explanations:

The given logarithmic expression is:

$(1)/(9)\ln (x+2)^9-(1)/(4)\lbrack\ln (x^(16))-\ln (x^2+6)^4\rbrack$

Expand the given expression

$(1)/(9)\ln (x+2)^9-(1)/(4)\ln (x^(16))-(1)/(4)\ln (x^2+6)^4$

It can be further simplified as:

$\begin{gathered} \ln (x+2)^{(9)/(9)}-\ln (x^{(16)/(4)})-\ln (x^2+6)^{(4)/(4)} \\ \ln (x+2)-\ln (x^4)-\ln (x^2+6) \end{gathered}$

The expression can be written as a single logarithm as shown below:

$\ln ((x+2))/(x^4(x^2+6))$

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