Question

If $2^{1998}–2^{1997}–2^{1996}+2^{1995}=\mathrm{K}{2}^{1995}$, then the value of $K$is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C

$3$

Explanation for correct option:

Divide by $2^{1995}$on both sides.

Given: $2^{1998}–2^{1997}–2^{1996}+2^{1995}=K{2}^{1995}$

$\frac{2^{1998}}{2^{1995}}–\frac{2^{1997}}{2^{1995}}–\frac{2^{1996}}{2^{1995}}+\frac{2^{1995}}{2^{1995}}=K\frac{2^{1995}}{2^{1995}}$

$2^3–2^2–2^1+2^0=K$

$$\begin{gathered} \Rightarrow K=2^3–2^2–2^1+2^0 \\ \Rightarrow K=8-4-2+1 \\ \therefore K=3 \end{gathered}$$

Hence, the value of $K$ is $3$.

Option $C$ is the correct answer.