Question

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

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

Answer 1

The correct option is C $25\sqrt{5}$

Given,$4^x-4^{x-1}=24$
$\Rightarrow 4^x(1-\frac{1}{4})=24$
$\Rightarrow 4^x=24\times \frac{4}{3}$
$\Rightarrow 4^x=32=4^2\times 2$
$\Rightarrow 4^x=4^2\times 4^{\frac{1}{2}}=4^{\frac{5}{2}}$
$\Rightarrow x=\frac{5}{2}$
Now, $(2x{)}^x=(2\times \frac{5}{2}{)}^{\frac{5}{2}}$
$=5^{\frac{5}{2}}=5^{2+\frac{1}{2}}$
$=5^2\times \sqrt{5}$
$=25\sqrt{5}$
Hence, Option C is correct.