Question

If $4^x-4^{x-1}=48$, then $(2x{)}^x$ equals

• A. $216$
• B. $156$
• C. $64$
• D. $125$

Answer 1

The correct option is A $216$

Given : $4^x-4^{x-1}=48$
$\Rightarrow 4^{x-1}(4-1)=48$
$\Rightarrow 4^{x-1}=\frac{48}{3}$
$\Rightarrow 4^{x-1}=16$
$\Rightarrow (2^2{)}^{x-1}=2^4$
On comparing both the sides , we get
$2(x-1)=4$
$\Rightarrow (x-1)=\frac{4}{2}$
$\Rightarrow x=3$
$\therefore (2x{)}^x=(2\times 3{)}^3$
$=(6{)}^3$
$=\left(216\right)$

Hence,(c) is correct answer.