Question

4^x - 4^x-1 = 24 , then what is the value of (2x) ^x​

Answer 1

Answer:

$(2x)^x=25\sqrt{5}$

Step-by-step explanation:

$4^x-4^{x-1}=24 (Given) \\\implies4^x-\frac{4^x}{4}=24\\\implies4^x(1-\frac{1}{4})=24\\\implies4^x\times\frac{3}{4}\\\\\implies4^x=\frac{24\times4}{3} =32\\\\\therefore 2^{2x}=32=2^5\\\implies 2x=5\\\implies x=\frac{5}{2}=2.5$

Now

$(2x)^x=(2\times\frac{5}{2})^\frac{5}{2}=(5)^\frac{5}{2}=\sqrt{5\times5\times5\times5\times5}=25\sqrt{5}$