Question

Choose the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}{2}^n=4096,\mathrm{then}{2}^{n-5}= \\ \left(\mathrm{a}\right)128\left(\mathrm{b}\right)64\left(\mathrm{c}\right)256\left(\mathrm{d}\right)32 \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},2^n=4096 \\ \Rightarrow 2^{\mathit{n}}=2^{12} \\ \mathrm{Comparing}\mathrm{the}\mathrm{exponent}\mathrm{of}\mathrm{both}\mathrm{the}\mathrm{sides},\mathrm{we}\mathrm{get} \\ n=12 \\ \mathrm{Now},2^{n-5}=2^{12-5} \\ =2^7 \\ =128 \end{gathered}$$

Hence, the correct alternative is option (a).