Question

using log tables, calculate ${\left[\frac{5.3\times 2.843}{0.80341}\right]}^{\frac{1}{3}}$
Using Log tables calculate $\frac{{\left(4.63\right)}^2\times {\left(0.08341\right)}^{\frac{2}{5}}}{{\left(0.006743\right)}^{\frac{1}{4}}}$

Answer 1

$\left(i\right)$Let $x={\left[\frac{5.3\times 2.843}{0.80341}\right]}^{\frac{1}{3}}$

$\Rightarrow \log x=\log \left[{\left(\frac{5.3\times 2.843}{0.80341}\right)}^{\frac{1}{3}}\right]$

$\Rightarrow \log x=\frac{1}{3}\log \left(\frac{5.3\times 2.843}{0.80341}\right)$

$\Rightarrow \log x=\frac{1}{3}[\log 5.3+\log 2.843-\log 0.80341]$

$=\frac{1}{3}[0.7242+0.4537+0.0950]$

$=\frac{1}{3}\times 1.2729=0.4243‬$

$\left(ii\right)y=\frac{{\left(4.63\right)}^2\times {\left(0.08341\right)}^{\frac{2}{5}}}{{\left(0.006743\right)}^{\frac{1}{4}}}$

$\log y=\log \left[\frac{{\left(4.63\right)}^2\times {\left(0.08341\right)}^{\frac{2}{5}}}{{\left(0.006743\right)}^{\frac{1}{4}}}\right]$

$=2\log \left(4.63\right)+\frac{2}{5}\log \left(0.08341\right)-\frac{1}{4}\log \left(0.006743\right)$

$=2\times 0.6655+\frac{2}{5}\times -1.0787-\frac{1}{4}\times -2.17114$

$=1.331‬-0.43148+0.542785‬=1.442305$