(a)(i) Given that (log_{10} 5 = 0.699) and (log_{10} 3 = 0.477), find (log_{10} 45), without using Mathematical tables.
(ii) Hence, solve (x^{0.8265} = 45).
(b) Use Mathematical tables to evaluate (sqrt{frac{2.067}{0.0348 times 0.538}})
Explanation
(a)(i) (log_{10} 45 = log_{10} (3 times 3 times 5))
= (log_{10} (3^{2} times 5))
= (log_{10} 3^{2} + log_{10} 5)
= (2 log_{10} 3 + log_{10} 5)
= (2(0.477) + 0.699)
= (0.954 + 0.699 = 1.653)
(ii) (x^{0.8265} = 45)
Taking the log of both sides,
(log_{10} x^{0.8265} = log_{10} 45)
(0.8265 log_{10} x = log_{10} 45)
(log_{10} x = frac{1.653}{0.8265})
(log_{10} x = 2)
(x = 10^{2} = 100)
(b) (sqrt{frac{2.067}{0.0348 times 0.538}})
No | Log |
2.067 | (0.0348) = 0.3513 – |
0.0348 |
(bar{2}.5416 +) |
0.538 | (bar{1}.7308) |
(bar{2}.2724) = (bar{2}.2724) | |
= (2.0789 div 2 = 1.0395) | |
Antilog – 10.95 |
(therefore sqrt{frac{2.067}{0.0348 times 0.538}} = 10.95)