Question

${\log }_{10}x+{\log }_{10}y\ge 2$, then the smallest possible value of $x+y$ is

• A. $10$
• B. $30$
• C. $20$
• D. None of these

Answer 1

The correct option is C $20$

${log}_{10}x+{log}_{10}y=$ $lo{g}_{10}\left(xy\right)\ge 2$,
Thus, $xy\ge 100$
Given the product of two numbers ,addition of two number is smallest when they are equal.
$x^2\ge 100$
Therefore, smallest value of $x+y=20$
Hence, option 'C' is correct.