corive Condensed form
a) $\frac{1}{9}\left(\log _{3} z+2 \log _{3} y\right)=$
b) $\quad \ln x+2 \ln y+5 \ln z=$

Step 1 ：Given the expression: \(\frac{1}{9}(\log _{3} z+2 \log _{3} y)\)

Step 2 ：Simplify the expression as follows: \(\frac{1}{9}\log _{3} z + \frac{2}{9}\log _{3} y\)

Step 3 ：Using the properties of logarithms, rewrite the expression as: \(\log _{3} z^{\frac{1}{9}} + \log _{3} y^{\frac{2}{9}}\)

Step 4 ：Combine the two logarithms into one: \(\log _{3} (z^{\frac{1}{9}}y^{\frac{2}{9}})\)

Step 5 ：Given the expression: \(\ln x+2 \ln y+5 \ln z\)

Step 6 ：Simplify the expression as follows: \(\ln x + \ln y^2 + \ln z^5\)

Step 7 ：Using the properties of natural logarithms, combine the three logarithms into one: \(\ln (x y^2 z^5)\)

Step 8 ：Final Answer: a) \(\boxed{\log _{3} (z^{\frac{1}{9}}y^{\frac{2}{9}})}\) b) \(\boxed{\ln (x y^2 z^5)}\)