Question

If $4^x-4^{x-1}=24$, then the value of $(2x{)}^x$ is:

• A. $5^{\frac{5}{2}}$
• B. $5^{\frac{1}{3}}$
• C. $4^{\frac{1}{2}}$
• D. $6^{\frac{1}{2}}$

Answer 1

The correct option is A $5^{\frac{5}{2}}$

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

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

$\Rightarrow 4^x(1-\frac{1}{4})=24$

$\Rightarrow 4^x=32\Rightarrow 2^{2x}=2^5$

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

Put $x=\frac{5}{2}$ in $(2x{)}^x$

$(2x{)}^x=(5{)}^{\frac{5}{2}}$