Question

The value of $({\log }_{10}8+{\log }_{10}25+2{\log }_{10}3-{\log }_{10}18)$ is equal to

• A. $1$
• B. $-3$
• C. $2$
• D. $-4$

Answer 1

Answer: (C)

$2$

$x={\log }_{10}8+{\log }_{10}25+2{\log }_{10}3-{\log }_{10}18$

$\therefore x={\log }_{10}8+{\log }_{10}25+{\log }_{10}{3}^2-{\log }_{10}18$ . ($\log a^b=b\log a$)

$\therefore x={\log }_{10}\frac{1800}{18}$ ($\log \frac{a}{b}=\log a-\log b$, )

$\log a.b=\log a+\log b$

$x=2$