Question

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

• A. 0
• B. 1
• C. 2
• D. 10

Answer 1

The correct option is B 1

${\left[lo{g}_{10}\left(5lo{g}_{10}100\right)\right]}^2$
$\because lo{g}_{10}100=2$
$\Rightarrow {\left[lo{g}_{10}(5\times 2)\right]}^2$
$\Rightarrow {\left[lo{g}_{10}10\right]}^2$
$\because lo{g}_{10}10=1$
$\Rightarrow {\left[1\right]}^2=1$