Question

If 4^x - 4^x-1 = 24, then (2x)^x is​

Answer 1

Answer:

hi made your answer is 25√5

love you ❤️ and have a good day bro or sis

thanks for points and don't forget to mark me as a brainliest

Answer 2

GIVEN:-

• $\rm{4^x-4^{x-1}-4=24}$

TO FIND:-

• $\rm{(2x)^x}$

Now,

$\implies\rm{(2)^{2x}-2^{2x-2}=24}$

$\implies\rm{2^{2x}(1-\dfrac{1}{4})=24}$

$\implies\rm{2^{2x}\times{\dfrac{3}{4}}=24}$

$\implies\rm{2^{2x}\times{3}=96}$

$\implies\rm{2^{2x}=32}$

$\implies\rm{2^{2x}=2^{5}}$

As Bases are same, equating the powers

$\implies\rm{2x=5}$

$\implies\rm{x=\dfrac{5}{2}}$

Now,Atq

$\implies\sf{(2x)^x}$

$\implies\sf{2\times{\dfrac{5}{2}}^\frac{5}{2}}$

$\implies\sf{ 5^\frac{5}{2}}$

$\implies\sf{25\sqrt{5}}$.

Hence, The value of $\rm{(2x)^x}$ is

$\sf{25\sqrt{5}}$.