To four decimal places, $\log _{10} 5=0.6990$ and $\log _{10} 9=0.9542$. Evaluate the logarithm $\log _{10} \frac{5}{9}$ using these values. Do not use a calculator. \[ \log _{10} \frac{5}{9}=\square \] (Simplify your answer.)

Step 1 ：Given: \(\log_{10} 5 = 0.6990\) and \(\log_{10} 9 = 0.9542\)

Step 2 ：Using the property of logarithms, \(\log_{10} \left(\frac{5}{9}\right) = \log_{10} 5 - \log_{10} 9\)

Step 3 ：Substituting the given values, \(\log_{10} \left(\frac{5}{9}\right) = 0.6990 - 0.9542\)

Step 4 ：Simplifying the subtraction, \(\log_{10} \left(\frac{5}{9}\right) = -0.2552\)

Step 5 ：Therefore, \(\boxed{\log_{10} \left(\frac{5}{9}\right) = -0.2552}\)