Question

2x^x equals to what. Please solve this.​

Answer 1

$\sf{Answer: \ 5^{\frac{5}{2}}}$

$4^x-4^{x-1}=24 \\ \\ 4^{x-1}(4 - 1)=24\ \ \ \ \ [4^{x-1}\cdot 4^1=4^{x-1+1}=4^x] \\ \\ 4^{x-1} \cdot 3=24 \\ \\ 4^{x-1}=8 \\ \\ 4^x\div4=8 \\ \\ 4^x=32$

$(2^2)^x=32 \\ \\ 2^{2x}=2^5 \\ \\ \\ 2x=5 \\ \\ x=\frac{5}{2}$

$(2x)^x \\ \\ 2^x \cdot x^x \\ \\ \sqrt{32}\ \cdot \ (\frac{5}{2})^{\frac{5}{2}}\ \ \ \ \ [2^{2x}=(2^x)^2=32\ \ \ ; \ \ \ 2^x=\sqrt{32}] \\ \\ \sqrt{32} \ \cdot\ ((\frac{5}{2})^5)^\frac{1}{2} \\ \\ \sqrt{32} \ \cdot \ (\frac{5^5}{2^5})^{\frac{1}{2}} \\ \\ \sqrt{32}\ \cdot \ \sqrt{\frac{5^5}{32}} \\ \\ \sqrt{32 \cdot \frac{5^5}{32}} \\ \\ \sqrt{5^5} \\ \\ 5^{\frac{5}{2}} \ = \ 5^x$

$\therefore\ (2x)^x=5^x$

$[\sf{Note: Telling to some idiotic fellows not to spam and consider my answer as wrong without having knowledge about the method I used. Telling because I had had such an experience. ]}$

$\sf{Hope this helps you. \\ \\ Please mark it as the brainliest.}$

$\sf{Thank you. :-)}$

         

Answer 2

4X - 4 X-1 = 24 i.e.,
(2)2x - (2)2(x -1) = 24
i.e., (2)2x - (2)2x -2) = 24 
i.e., (2)2x - (2)2x /4= 24 
On simplifying, we get
 (2)2x = 32 = 25 
So, 2x = 5
 i.e, x = 5/2 
Now,  (2x)x = (2 x 5/2)5/2        
=  (5)5/2          
 = 25 (5)1/2      
  = 25√5