(a) With the aid of four- figure logarithm tables, evaluate \((0.004592)^{\frac{1}{3}}\).
(b) If \(\log_{10} y + 3\log_{10} x = 2\), 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),
\(- 8y - 15y = 84 - 15\)
\(- 23y = 69 \implies y = -3\)
\(3x - 2y = 21 \implies 3x - 2(-3) = 21\)
\(3x + 6 = 21 \implies 3x = 15\)
\(x = 5\)