Question 5: Find the values of the following with the help of logarithm table:
\((iii)\) \(\quad\) \(\large{\frac{( 20.46)^{2} \times ( 2.4122)}{754.3} }\)
Solution:
Let
\[x=\frac{( 20.46)^{2} \times ( 2.4122)}{754.3}\]
Taking logarithm on both sides, we get
\[\log x=\log\left(\frac{( 20.46)^{2} \times ( 2.4122)}{754.3}\right)\]
\[
\begin{align*}
&=\small{\log( 20.46)^{2} +\log 2.4122-\log 754.3}\\
&=\small{2\log 20.46+\log 2.4122-\log 754.3}\\
&=2( 1.3109) +0.3824-2.8775\\
&=0.1267\\
\end{align*}
\]
Taking antilog on both sides, we get
\[
\begin{align*}
\text{anti-log}(\log x) &=\text{anti-log}( 0.1267)\\
x&=1.339\\
\end{align*}
\]