Question

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

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

Answer 1

The correct option is C $(5{)}^{\frac{5}{2}}$

$4^x-4^{x-1}=24$
Taking $4^x$ common, we get $4^x(1-\frac{1}{4})=24$

$4^x\left(\frac{3}{4}\right)=24$ or $4^x=32$
Expressing in terms of 2,
$2^{2x}=32$or $2^{2x}=2^5$

$\therefore x=2.5$
So, ${(2\times 2.5)}^{2.5}=5^{2.5}$