Question

If ${\log }_{2}a<5$, then which of the following can be true?

• A. $a=32$
• B. $a=256$
• C. $a=16$
• D. $a=64$

Answer 1

The correct option is C $a=16$

Using the property
${\log }_{m}a<b\Rightarrow \{\begin{array}{cc}a<m^b,& \text{if}m>1\\ a>m^b,& \text{if}0<m<1\end{array}$

Here ${\log }_{2}a<5$ and $m>1$
$\Rightarrow a$ should be less than $2^5$.
$\Rightarrow a<32$
Therefore from the given options, the answer is $a=16$