Question

Without using log tables, evaluate $2{\log }_{10}5+{\log }_{10}5-\frac{1}{2}{\log }_{10}4$

Answer 1

$2{\log }_{10}5+{\log }_{10}5-\frac{1}{2}{\log }_{10}^4$

$\Rightarrow 2{\log }_{10}\left(5\right)+{\log }_{10}\left(5\right)-{\log }_{10}\left(2\right)$

$\Rightarrow 3{\log }_{10}\left(5\right)-{\log }_{10}2$

$\Rightarrow 3\left({\log }_{10}\left(10/2\right)\right)-{\log }_{10}\left(2\right)$

$\Rightarrow 3{\log }_{10}10-3{\log }_{10}\left(2\right)-\log \left(2\right)$

$\Rightarrow 3-4\log 2=1.79588$