Question

Solve: $2{\log }_{10}5+{\log }_{10}8-\frac{1}{2}{\log }_{10}4$

Answer 1

Now,

$2{\log }_{10}5+{\log }_{10}8-\frac{1}{2}{\log }_{10}4$

$={\log }_{10}{5}^2+{\log }_{10}8-{\log }_{10}\sqrt{4}$ [ Using rules of logarithm]

$={\log }_{10}\left(\frac{25\times 8}{2}\right)$ [ Using rules of logarithm]

$={\log }_{10}{10}^2$

$=2$.