Question

Express as a single logarithm: $2+\frac{1}{2}{\log }_{10}9-2{\log }_{10}5$

• A. ${\log }_{10}12$
• B. ${\log }_{12}10$
• C. $2{\log }_{10}3$
• D. $3{\log }_{10}2$

Answer 1

The correct option is A ${\log }_{10}12$

$2={\log }_{10}100$

Then,

$2+\frac{1}{2}{\log }_{10}9-2{\log }_{10}5$

$={\log }_{10}100+{\log }_{10}3-{\log }_{10}25$

$={\log }_{10}\frac{300}{25}$ .... ($\because {\log }_{10}m+n={\log }_{10}\left(mn\right)$ and ${\log }_{10}m-n={\log }_{10}\left(m/n\right)$ )

$={\log }_{10}12$