Question

Evaluate the following using log tables (5.364)^(3)×(49.76)^(1)/(2)/(83.28)(1)/(2)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:\dfrac{ {(5.364)}^{3} \times \sqrt{49.76} }{ \sqrt{83.28} }$

Let assume that

$\rm :\longmapsto\:y = \dfrac{ {(5.364)}^{3} \times \sqrt{49.76} }{ \sqrt{83.28} }$

Taking log on both sides, we get

$\rm :\longmapsto\:logy =log\bigg( \dfrac{ {(5.364)}^{3} \times \sqrt{49.76} }{ \sqrt{83.28} }\bigg)$

We know,

$\boxed{ \bf{ \: log( \frac{x}{y} ) = logx - logy}}$

So, using this,

$\rm \: = \: \:log( {(5.364)}^{3} \times \sqrt{49.76}) - log \sqrt{83.28}$

We know,

$\boxed{ \bf{ \: log(xy ) = logx + logy}}$

So, using this,

$\rm \: = \: \:log( {5.364)}^{3} +log \sqrt{49.76} - log \sqrt{83.28}$

We know,

$\boxed{ \bf{ \: log( {x}^{y} ) =y logx}}$

So, using this,

$\rm \: = \: \:3log(5.364) + \dfrac{1}{2}log(49.76) - \dfrac{1}{2}log(83.28)$

Now, using log tables,

$\rm :\longmapsto\:log(5.364) = 0.7295$

$\rm :\longmapsto\:log(49.76) = 1.6969$

$\rm :\longmapsto\:log(83.28) = 1.9205$

So, on substituting these values,

$\rm \: = \: \:3(0.7295) + \dfrac{1}{2}(1.6969) - \dfrac{1}{2}(1.9205)$

$\rm \: = \: \:2.1885 + 0.84845 - \dfrac{1}{2}(1.9205) - 0.96025$

$\rm \: = \: \:2.0767$

$\bf\implies \:logy = \: \:2.0767$

So,

$\bf\implies \:y = \: antilog( \:2.0767)$

$\rm \: = \: \: {10}^{2} \times 1.193$

$\rm \: = \: \:119.3$

Hence,

$\boxed{\bf :\longmapsto\:\dfrac{ {(5.364)}^{3} \times \sqrt{49.76} }{ \sqrt{83.28} } = 119.3 \quad}$