(a) If \(\log_{10} (3x – 1) – \log_{10} 2 = 3\), find the value of x.
(b) Use logarithm tables to evaluate \(\sqrt{\frac{0.897 \times 3.536}{0.00249}}\), correct to 3 significant figures.
Explanation
(a) \(\log_{10} (3x - 1) - \log_{10} 2 = 3\)
\(\log_{10} (\frac{3x - 1}{2}) = 3\)
\(\implies \frac{3x - 1}{2} = 10^{3} = 1000\)
\(\implies 3x - 1 = 2000\)
\(3x = 2000 + 1 = 2001\)
\(x = \frac{2001}{3} = 667\)
(b)
| No | Log |
| 0.8972 | \(\bar{1}.9528\) + |
| 3.536 | \(0.5485\) |
| = 0.5013 - | |
| 0.00249 | \(\bar{3}.3962\) |
| Antilog - 35.70 | \(3.1051 \div 2 = 1.5526\) |
\(\therefore \sqrt{\frac{0.8972 \times 3.536}{0.00249}} = 35.70\)