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 $\log _{a} 27$.
\[
\log _{a} 27=
\]

Answer

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Answer

Final Answer: $\boxed{1.431}$

Steps

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: $\boxed{1.431}$