(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) \(\frac{\log 81}{\log \frac{1}{3}}\)
= \(\frac{\log 3^{4}}{\log 3^{-1}}\)
= \(\frac{4 \log 3}{-1 \log 3}\)
= \(-4\)