Question

If $2^m-2^{m-1}-4=0.$Then value of $m^m$ is:

• A. $4$
• B. $27$
• C. $6$
• D. $29$

Answer 1

The correct option is B

$27$

Solution:

Solving the expression:

$2^m-2^{m-1}-4=0.$

$$\begin{gathered} \Rightarrow 2^m-2^{m-1}=4 \\ \Rightarrow 2^{m-1}(2^1-1)=2^2(\because 2^2=4,\mathrm{taking}{2}^{m-1}\mathrm{as}\mathrm{common}) \\ \Rightarrow 2^{m-1}\times 1=2^2 \\ \Rightarrow 2^{m-1}=2^2 \\ \therefore m-1=2\left(\mathrm{Equating}\mathrm{the}\mathrm{powers}\mathrm{as}\mathrm{the}\mathrm{base}\mathrm{on}\mathrm{both}\mathrm{sides}\mathrm{are}\mathrm{equal}\right) \\ \Rightarrow m=3 \\ \therefore m^m=3^3 \\ =27 \end{gathered}$$

Final answer: Hence, the correct option is (B).