Question

QUESTION ELEVEN (11) LAST PART ONLYQUESTION 11 NOT Q0 NOT 12

Answer 1

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))`