Question

What is the value of $\left[{\log }_{10}\right(5{\log }_{10}100){]}^2$?

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

The value of $\left[{\log }_{10}\right(5{\log }_{10}100){]}^2$ is
$=\left[{\log }_{10}\right(5{\log }_{10}{10}^2){]}^2$

$=\left[{\log }_{10}\right(10{\log }_{10}10){]}^2$ .....As $\log a^m=m\log a$

$=\left[{\log }_{10}\right(10\times 1){]}^2$ ....As ${\log }_{a}a=1$

$=[{\log }_{10}10{]}^2$

$=[1{]}^2=1$