Question

if $4^x-4^{x-1}=24$ then find the value of $(2x{)}^x.$

Answer 1

$4^x-4^{x-1}=24$

$\Rightarrow 4^x-\frac{4^x}{4}=24$

$\frac{3}{4}\left(4^x\right)=24$

$\Rightarrow \left(2^{2x}\right)=32$

$\Rightarrow 2^{2x}=2^5$

$2x=5$

$\Rightarrow x=\frac{5}{2}$

$(2x{)}^x=(5{)}^{\frac{5}{2}}\Rightarrow (\sqrt{5}{)}^5\Rightarrow 5.5\times \sqrt{5}\Rightarrow 25\sqrt{5}$

$\therefore (2x{)}^x=25\sqrt{5}$