Question

If $4^x-4^{x-1}=24,then(2x{)}^x$ equals

• A. $5\sqrt{5}$
• B. $\sqrt{5}$
• C. $25\sqrt{5}$
• D. 125

Answer 1

The correct option is C

$25\sqrt{5}$

$4^x-4^{x-1}=24\Rightarrow 4^x-\frac{4^x}{4^1}=244x(1-\frac{1}{4})=24\Rightarrow 4^x\times \frac{3}{4}=24\Rightarrow 4^x=\frac{24\times 4}{3}=32(2^2{)}^x=32=(2{)}^5\Rightarrow 2^{2x}=2^{5}Comparing,weget2x=5\Rightarrow x=\frac{5}{2}\therefore (2x{)}^x={(2\times \frac{5}{2})}^{\frac{5}{2}}=(5{)}^{\frac{5}{2}}=\sqrt{5^5}=\sqrt{5\times 5\times 5\times 5\times 5}=5\times 5\sqrt{5}=25\sqrt{5}$