(a) Using logarithm table, evaluate (frac{sqrt[3]{1.376}}{sqrt[4]{0.007}}) correct to three significant figure.
(b) Without using Mathematical tables, find the value of (frac{log 81}{log frac{1}{3}}).
Explanation
(a)
| No | Log |
| (sqrt[3]{1.376}) | (0.1386 div 3 ) = (0.0462) |
| (sqrt[4]{0.007}) | (bar{3}.8451 div 4) = (bar{1}.4613) |
| (frac{sqrt[3]{1.376}}{sqrt[4]{0.007}}) = | (0.5849) |
| Antilog = 3.845 |
(therefore frac{sqrt[3]{1.376}}{sqrt[4]{0.007}} approxeq 3.85) (to 3 s.f)
(b) (frac{log 81}{log frac{1}{3}})
= (frac{log 3^{4}}{log 3^{-1}})
= (frac{4 log 3}{-1 log 3})
= (-4)