Question

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

Answer 1

Answer: 5²⁻⁵

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=(3)/(2)\\\\\\x=(5)/(2)\quad \rightarrow x=2.5`

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