Question

Express as a single logarithm

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

• A. $lo{g}_{10}12$
• B. $lo{g}_{10}2$
• C. $lo{g}_{10}5$
• D. $lo{g}_{10}7$

Answer 1

The correct option is A

$lo{g}_{10}12$

$2+\frac{1}{2}lo{g}_{10}9-2lo{g}_{10}5$ = $lo{g}_{10}100+lo{g}_{10}{9}^{\frac{1}{2}}-lo{g}_{10}{5}^2$

= $lo{g}_{10}100+lo{g}_{10}3-lo{g}_{10}25$

=$lo{g}_{10}\frac{100\times 3}{25}$

=$lo{g}_{10}12$