Question

Type the correct answer in each box. If necessary, use / for the fraction bar.Evaluate these logarithms using the properties of logarithms.

Answer 1

Using the properties of logarithms, we have:

`\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}`
`\begin{gathered} \log _28-\log _24=\log _2((8)/(4))(\text{ Using the quotient property)} \\ \log _2(2)\text{ (Dividing)} \\ 1\text{ (Solving the logarithm)} \\ \text{Answer: 1} \end{gathered}`
`\begin{gathered} \log _55\cdot5^{(1)/(3)}=\log _55^{1+(1)/(3)}\text{ (Using the product property of exponents)} \\ \log _55^{(4)/(3)}\text{ (Adding fractions)} \\ (4)/(3)\log _55\text{ (Using the power property of logarithms)} \\ (4)/(3)(1)\text{ (Solving the logarithm)} \\ (4)/(3)(\text{Multiplying)} \\ \text{Answer: }(4)/(3) \end{gathered}`