Question

Simplify:${log}_{10}25+{log}_{10}4$

Answer 1

${\log }_{10}25+{\log }_{10}4$

$={\log }_{10}(25\times 4)$ since $\log x+\log y=\log \left(xy\right)$

$={\log }_{10}\left(100\right)$

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

$=2{\log }_{10}10$ since $\log a^m=m\log a$

$=2$ (since ${\log }_{a}a=1$)