Question

Find the value of N by using logorathim function
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Answer 1

Given Question :-

Using log table, to evaluate the following function

$\sf \: N = \dfrac{647.32 \times 0.00000147}{8.473 \times 64}$

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

Given that,

$\rm :\longmapsto\: \sf \: N = \dfrac{647.32 \times 0.00000147}{8.473 \times 64}$

can be rewritten as

$\rm :\longmapsto\: \sf \: N = \dfrac{6.4732 \times {10}^{2} \times 1.47 \times {10}^{ - 6} }{8.473 \times 6.4 \times 10}$

$\rm :\longmapsto\: \sf \: N = \dfrac{6.4732 \times 1.47 \times {10}^{ - 5} }{8.473 \times 6.4}$

Taking log on both sides

$\rm :\longmapsto\: \sf \:log N = log\bigg[ \dfrac{6.4732 \times 1.47 \times {10}^{ - 5} }{8.473 \times 6.4} \bigg]$

We know,

$\red{ \boxed{ \sf{ \:log(xy) = logx + logy}}} \\ \\ \red{ \boxed{ \sf{ \:log \frac{x}{y} = logx - logy}}} \: \: \: \\ \\ \red{ \boxed{ \sf{ \:log {x}^{y} = ylogx}}} \: \: \: \: \: \: \: \: \: \:$

So, using these Identities, we have

$\rm :\longmapsto\:logN = log6.4732 + log1.47 - 5log10 - log8.473 - log6.4$

$\rm \:  =  \: 0.8111 + 0.1673 - 5 - 0.9281 - 0.8062$

$\rm \:  =  \: -5.7559$

$\rm \:  =  \: -5 - 1 + 1 - 0.7559$

$\rm \:  =  \: -6 +0.2441$

$\rm \:  =  \: \bar{6}.2441$

So,

$\rm :\implies\:logN  =  \: \bar{6}.2441$

Therefore,

$\rm :\implies\:N  =  \:antilog( \bar{6}.2441)$

$\rm :\longmapsto\:N = {10}^{ - 6} \times 1.754$

$\bf\implies \:N = 0.000001754$

Hence,

$\red{ \boxed{ \sf{ \:\sf \: N = \dfrac{647.32 \times 0.00000147}{8.473 \times 64} = 0.000001754}}}$