Question

The value of ${\int }_0^2(x-{\log }_{2}a)dx=2{\log }_2\left(\frac{2}{a}\right)$ for which of the following conditions?

• A. $a>0$
• B. $a>2$
• C. $a=4$
• D. $a=8$

Answer 1

The correct option is A $a>0$

${\int }_0^2(x-{\log }_{2}a)dx=2{\log }_2(\frac{2}{a})$

The solution exists only if function is defined.

$x-{\log }_{2}a⟶$ defined

$x⟶$ is defined for all values

But ${\log }_{2}a⟶$ defined for all values

But ${\log }_{2}a⟶$ defined for only a>0$

$\therefore \log \left(0\right)$ and $\log \text{(negative values)})⟶$ not defined

Hence, required condition is $a>0$.