Answer:
[tex] \dfrac{1}{2} \ln (y - 10) - \dfrac{9}{2} \ln (y + 5) [/tex]
Step-by-step explanation:
[tex] \ln \sqrt{\dfrac{(y^2 - 100)(y + 5)^9}{y + 10}} = [/tex]
[tex] = \ln \sqrt{\dfrac{(y + 10)(y - 10)(y + 5)^9}{y + 10}} [/tex]
[tex] = \ln [(y - 10)(y + 5)^9]^{\frac{1}{2}} [/tex]
[tex] = \dfrac{1}{2} \ln [(y - 10)(y + 5)^9] [/tex]
[tex] = \dfrac{1}{2} [\ln (y - 10) - \ln (y + 5)^9] [/tex]
[tex] = \dfrac{1}{2} [\ln (y - 10) - 9 \ln (y + 5)] [/tex]
[tex] = \dfrac{1}{2} \ln (y - 10) - \dfrac{9}{2} \ln (y + 5) [/tex]
