Question

What is the value of $\frac{1}{2}{\log }_{10}25-2{\log }_{10}3+{\log }_{10}18$?

• A. $2$
• B. $3$
• C. $1$
• D. $0$

Answer 1

The correct option is C $1$

The value of $\frac{1}{2}{\log }_{10}25-2{\log }_{10}3+{\log }_{10}18$ is
$={\log }_{10}(25{)}^{1/2}-{\log }_{10}(3{)}^2+{\log }_{10}18$
$={\log }_{10}5-{\log }_{10}9+{\log }_{10}18$
$={\log }_{10}(\frac{5}{9}\times 18)$

$={\log }_{10}10$ ....Using the identity ${\log }_{a}a=1$

$=1$