Question

4^x-4^x-1=24,then find (2x)^x

Answer 1

Answer:  5²⁻⁵

Step-by-step explanation:

$4^x-4^{x-1}=24\\\\\\3(4^{x-1})=24\\\\\\4^{x-1}=8\\\\\\2^{2(x-1)}=2^3\\\\\\2(x-1)=3\\\\\\x-1=\dfrac{3}{2}\\\\\\x=\dfrac{5}{2}\quad \rightarrow x=2.5$

$(2x)^x\quad =(2\cdot 2.5)^{2.5}\quad =\large\boxed{5^{2.5}}$