(a) With the aid of four- figure logarithm tables, evaluate ((0.004592)^{frac{1}{3}}).
(b) If (log_{10} y + 3log_{10} x = 2), express y in terms of x.
(c) Solve the equations : (3x – 2y = 21)
(4x + 5y = 5).
Explanation
(a)
| No | Log |
| 0.004592 | (bar{3}.6620) |
| ((0.004592)^{frac{1}{3}}) | (frac{bar{3}.6620}{3} = bar{1}.2207) |
Antilog of (bar{1}.2207 = 0.1663)
(b) (log_{10} y + 3 log_{10} x = 2)
(log_{10} y + log_{10} x^{3} = 2)
(log_{10} (yx^{3}) = 2)
(yx^{3} = 10^{2})
(yx^{3} = 100)
(y = frac{100}{x^{3}})
(c) (3x – 2y = 21 …. (1))
(4x + 5y = 5 ….. (2))
Multiply (1) by 4 and (2) by 3,
(12x – 8y = 84 …. (1a))
(12x + 15y = 15 … (2a))
(1a) – (2a),
(- 8y – 15y = 84 – 15)
(- 23y = 69 implies y = -3)
(3x – 2y = 21 implies 3x – 2(-3) = 21)
(3x + 6 = 21 implies 3x = 15)
(x = 5)