Question

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

• A. ${\log }_{10}12$
• B. ${\log }_{12}10$
• C. ${\log }_{10}15$
• D. ${\log }_{15}10$

Answer 1

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

$2+\frac{1}{2}{\log }_{10}9-2{\log }_{10}5$ ...(given)
$=2{\log }_{10}10+{\log }_{10}{9}^{\frac{1}{2}}-{\log }_{10}{5}^2$

$={\log }_{10}100+{\log }_{10}3-{\log }_{10}25$
$={\log }_{10}\frac{100\times 3}{25}$
$={\log }_{10}12$