(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)