lomework Question 15, 5.2.29 Use properties of logarithms with the given approximations to evaluate the expression. $\log _{a} 3 \approx 0.477$ and $\log _{a} 2 \approx 0.301$. Use one or both of these values to evaluate $\log _{a} 27$. \[ \log _{a} 27= \]

Step 1 ：Given that \(\log _{a} 3 \approx 0.477\) and \(\log _{a} 2 \approx 0.301\)

Step 2 ：We are asked to evaluate \(\log _{a} 27\)

Step 3 ：We know that 27 can be written as \(3^3\), so we can rewrite \(\log _{a} 27\) as \(3 \log _{a} 3\)

Step 4 ：Substitute the given value \(\log _{a} 3 \approx 0.477\) into the expression, we get \(3 \times 0.477\)

Step 5 ：Calculate the above expression to get the approximate value of \(\log _{a} 27\)

Step 6 ：\(\log _{a} 27 \approx 1.431\)

Step 7 ：Final Answer: \(\boxed{1.431}\)