Question

Find the value with the help of logarithm tables:
$5872\times 0.058$

Answer 1

Let $x=5872\times 0.058$

Taking $\log$ both sides, we have

$\log x=\log (5872\times 0.058)$

$\log x=\log 5872+\log 0.058(\because \log ab=\log a+\log b)$

$\log x=\log (58.72\times {10}^2)+\log (58\times 0^{-3})$

$\log x=\log 58.72+2+\log 58-3(\because \log 10=1)$

$\Rightarrow 1+\log x=\log 58.72+\log 58$

Using $\log$ table, we get

$\log 58.72=1.77$

$\log 58=1.76$

$\therefore 1+\log x=1.77+1.76$

$\Rightarrow \log x=3.53-1$

$\Rightarrow \log x=2.53$

$\Rightarrow x=\text{Antilog}\left(2.53\right)=338.84$

Therefore,

$5872\times 0.058\approx 338.84$