1. **Problem:** Find the values of the following logarithms to four decimal places using the property of logarithms and the given table values. 2. **Formula and rules:** - Use the logarithm product rule: $$\log_{10}(ab) = \log_{10} a + \log_{10} b$$ - Use the logarithm of powers of 10: $$\log_{10} 10^n = n$$ - Use the table values for logarithms of numbers between 1 and 10. 3. **Calculations:** (1) $$\log_{10} 2150 = \log_{10} (2.15 \times 10^3) = \log_{10} 2.15 + \log_{10} 10^3$$ From the table, $$\log_{10} 2.15 = 0.3324$$ So, $$\log_{10} 2150 = 0.3324 + 3 = 3.3324$$ (2) $$\log_{10} 184 = \log_{10} (1.84 \times 10^2) = \log_{10} 1.84 + \log_{10} 10^2$$ From the table, $$\log_{10} 1.84 = 0.2648$$ So, $$\log_{10} 184 = 0.2648 + 2 = 2.2648$$ (3) $$\log_{10} 15.8 = \log_{10} (1.58 \times 10^1) = \log_{10} 1.58 + \log_{10} 10^1$$ From the table, $$\log_{10} 1.58 = 0.1987$$ So, $$\log_{10} 15.8 = 0.1987 + 1 = 1.1987$$ (4) $$\log_{10} 0.0208 = \log_{10} (2.08 \times 10^{-2}) = \log_{10} 2.08 + \log_{10} 10^{-2}$$ From the table, $$\log_{10} 2.08 = 0.3181$$ So, $$\log_{10} 0.0208 = 0.3181 - 2 = -1.6819$$ 4. **Final answers:** - $$\log_{10} 2150 = 3.3324$$ - $$\log_{10} 184 = 2.2648$$ - $$\log_{10} 15.8 = 1.1987$$ - $$\log_{10} 0.0208 = -1.6819$$ These results use the logarithm properties and table values to find precise logarithms.