(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 \(\frac{\log 81}{\log \frac{1}{3}}\).
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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) \(\frac{\log 81}{\log \frac{1}{3}}\)
= \(\frac{\log 3^{4}}{\log 3^{-1}}\)
= \(\frac{4 \log 3}{-1 \log 3}\)
= \(-4\)
Source: Myschool Past Questions Archive (Record #54607)