Question 5: Find the values of the following with the help of logarithm table:
\((iv)\) \(\quad \)\(\large{\frac{\sqrt[3]{9.364} \times 21.64}{3.21}}\)
Solution:
Let
\[x=\frac{\sqrt[3]{9.364} \times 21.64}{3.21}\]
Taking logarithm on both sides, we get
\[\log x=\log\left(\frac{\sqrt[3]{9.364} \times 21.64}{3.21}\right)\]
\[
\begin{align*}
&=\small{\log\sqrt[3]{9.364} +\log 21.64-\log 3.21}\\
&=\small{\log( 9.364)^{\large{\frac{1}{3}}} +\log 21.64-\log 3.21}\\
&=\small{\frac{1}{3}\log( 9.364) +\log 21.64-\log 3.21}\\
&=\frac{1}{3}( 0.9715) +1.3353-0.5065\\
&=0.3238+1.3353-0.5065\\
&=1.1526\\
\end{align*}
\]
Taking antilog on both sides, we get
\[
\begin{align*}
\text{anti-log}(\log x) &=\text{anti-log}( 1.1526)\\
x&=14.21\\
\end{align*}
\]