$\log _{a} 3=\log _{a} \frac{1}{3}$

Step 1 ：Let \(x = \log_a 3\) and \(y = \log_a \frac{1}{3}\)

Step 2 ：We have \(a^x = 3\) and \(a^y = \frac{1}{3}\)

Step 3 ：Since \(\log_a 3 = \log_a \frac{1}{3}\), we have \(x = y\)

Step 4 ：Now, we can write \(a^x = a^y\) as \(3 = \frac{1}{3}\)

Step 5 ：Multiplying both sides by 3, we get \(9 = 1\)

Step 6 ：This is a contradiction, so there is no value of \(a\) for which \(\log_a 3 = \log_a \frac{1}{3}\)

Step 7 ：\(\boxed{\text{No solution}}\)