Complete the table. $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & & & & & & & \
\hline
\end{array}$$
A) $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & 1 & 3 & 9 & 27 & - 27 & - 9 & - 3 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & 0 & 1 & 2 & 3 & 1 & 2 & 3 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & - 1 & - 3 & - 9 & - 27 & 27 & 9 & 3 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & 0 & 1 & 2 & 3 & - 1 & - 2 & - 3 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | c | c | }
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & \frac { 1 } { 3 } & 1 & 3 & 9 & \frac { 1 } { 9 } & \frac { 1 } { 27 } & \frac { 1 } { 81 } \
\hline
\end{array}$$

Question

Complete the table. $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & & & & & & & \
\hline
\end{array}$$
A) $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & 1 & 3 & 9 & 27 & - 27 & - 9 & - 3 \
\hline
\end{array}$$
B) $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & 0 & 1 & 2 & 3 & 1 & 2 & 3 \
\hline
\end{array}$$
C) $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & - 1 & - 3 & - 9 & - 27 & 27 & 9 & 3 \
\hline
\end{array}$$
D) $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & 0 & 1 & 2 & 3 & - 1 & - 2 & - 3 \
\hline
\end{array}$$
E) $$\begin{array} { | c | c | c | c | c | c | c | c | } 
\hline x & 1 & 3 & 3 ^ { 2 } & 3 ^ { 3 } & 3 ^ { - 1 } & 3 ^ { - 2 } & 3 ^ { - 3 } \
\hline \log 3 x & \frac { 1 } { 3 } & 1 & 3 & 9 & \frac { 1 } { 9 } & \frac { 1 } { 27 } & \frac { 1 } { 81 } \
\hline
\end{array}$$

Quizplus · Accepted Answer

Using the properties of logarithms, we have $\log_3 3^a=a$. Therefore, for the given values of $x$, we have:
$\log_3 3 = 1$
$\log_3 9 = 2$
$\log_3 27 = 3$
$\log_3 81 = 4$
$\log_3 \frac13 = -1$
$\log_3 \frac19 = -2$
$\log_3 \frac{1}{27} = -3$
Therefore, the correct values are given by choice (D).

Complete the Table A) B) C) D) E)