Question

If ${\log }_{10}8=0.90$
find $\log 0.125$

Answer 1

Given : $lo{g}_{10}8=\mathrm{0.90.}$

$\frac{1}{8}\times 8=1$

$\Rightarrow \left(0.25\right)\times 8=1$

apply log on both sides.

$\Rightarrow lo{g}_{10}\left(0.125\right)+lo{g}_{10}\left(8\right)=lo{g}_{10}\left(1\right)$

$\Rightarrow lo{g}_{10}\left(0.125\right)=0-lo{g}_{10}\left(8\right)$

$\Rightarrow lo{g}_{10}\left(0.125\right)=-\left(0.9\right)$