It is given that \( \log _{10} a=\frac{1}{3} \), where \( a>0 \) Find the value of (a) \( \log _{10}\left(\frac{1}{a}\right) \)

Given that \( \log_{10} a = \frac{1}{3} \), we want to find the value of \( \log_{10}\left(\frac{1}{a}\right) \). We can use the property of logarithms that states: \[ \log_{10}\left(\frac{1}{a}\right) = \log_{10}(1) - \log_{10}(a) \] Since \( \log_{10}(1) = 0\), we have: \[ \log_{10}\left(\frac{1}{a}\right) = 0 - \log_{10}(a) = -\log_{10}(a) \] Now, substituting in the value of \( \log_{10} a \): \[ \log_{10}\left(\frac{1}{a}\right) = -\frac{1}{3} \] Thus, the value of \( \log_{10}\left(\frac{1}{a}\right) \) is \[ \boxed{-\frac{1}{3}}. \]