Using the properties of logarithms, we have:
[tex]\begin{gathered} \log _39+\log _327=\log _3(9\cdot27)\text{ ( Using the product property)} \\ \log _3(243)(\text{Multiplying)} \\ \text{ }\log _3(243)=5\text{ (Solving the logarithm)} \\ \text{Answer: 5} \end{gathered}[/tex][tex]\begin{gathered} \log _28-\log _24=\log _2(\frac{8}{4})(\text{ Using the quotient property)} \\ \log _2(2)\text{ (Dividing)} \\ 1\text{ (Solving the logarithm)} \\ \text{Answer: 1} \end{gathered}[/tex][tex]\begin{gathered} \log _55\cdot5^{\frac{1}{3}}=\log _55^{1+\frac{1}{3}}\text{ (Using the product property of exponents)} \\ \log _55^{\frac{4}{3}}\text{ (Adding fractions)} \\ \frac{4}{3}\log _55\text{ (Using the power property of logarithms)} \\ \frac{4}{3}(1)\text{ (Solving the logarithm)} \\ \frac{4}{3}(\text{Multiplying)} \\ \text{Answer: }\frac{4}{3} \end{gathered}[/tex]
