Question 9: Find the values of the following with the help of logarithm table:
\((i)\) \(\quad\) \(\sqrt[3]{68.24}\)
Solution:
Let
\[x=\sqrt[3]{68.24}\]
Taking logarithm on both sides, we have
\[
\begin{align*}
\log x&=\log\sqrt[3]{68.24}\\
&=\log( 68.24)^{\frac{1}{3}}\\
&=\frac{1}{3}\log( 68.24)\\
&=\frac{1}{3}( 1.8340)\\
&=0.6113
\end{align*}
\]
Taking anti-logarithm on both sides, we have
\[
\begin{align*}
x&=\text{anti-logarithm}(0.6113)\\
x&=4.086
\end{align*}
\]