(a) \(\log_{10} 54 \) \(54 = 2 \times 3^{3}\) \(\log_{10} 54 = \log_{10} (2 \times 3^{3})\) = \(\log_{10} 2 + \log_{10} 3^{3}\) = \(\log_{10} 2 + 3\log_{10} 3\) = \(0.3010 + (3 \times 0.4771)\) = \(0.3010 + 1.4313\) = \(1.7323\) (b) \(\log_{10} 0.24\) \(0.24 = \frac{24}{100} = \frac{2^{3} \times 3}{100}\) \(\log_{10} 0.24 = \log_{10} 24 - \log_{10} 100\) \(\log_{10} (2^{3} \times 3) - \log_{10} (10^{2})\) \(\log_{10} 2^{3} + \log_{10} 3 - 2\log_{10} 10\) = \(3\log_{10} 2 + \log_{10} 3 - 2\) = \((3 \times 0.3010) + 0.4771 - 2\) = \(0.9030 + 0.4771 - 2\) = \(-0.6199\)