Log3 1/3=

To solve \( \log_3 \frac{1}{3} \), we can use the properties of logarithms.

We know that:

\[ \frac{1}{3} = 3^{-1} \]

Using this, we can rewrite the logarithm:

\[ \log_3 \frac{1}{3} = \log_3 (3^{-1}) \]

Using the power rule of logarithms, which states that \( \log_b (a^c) = c \cdot \log_b a \), we have:

\[ \log_3 (3^{-1}) = -1 \cdot \log_3 3 \]

Since \( \log_3 3 = 1 \), we find:

\[ \log_3 (3^{-1}) = -1 \cdot 1 = -1 \]

Thus:

\[ \log_3 \frac{1}{3} = -1 \]

The answer is \( -1 \).