Question

please solve the above question.... ​

Answer 1

$\mathbb{ANSWER}$

$\rm{x=\frac{11}{4}}$

$\mathbb{EXPLANATION}$

$\rm{\left(4\right)^{2x-1}\:-\left(16\right)^{x-1}=384}$

$\rm{\left(4\right)^{2x}\:4^{-1}\:-\left(4\right)^{2x}\:4^{-2}=384}$

$\boxed{\pink{a^{m+n}=a^m\times\:a^n}}$

$\underline{Take\:\left(4\right)^{2x}\:L.C.M\:\:We\:Have}$

$\implies{\rm{\left(4\right)^{2x}\left(4^{-1}-4^{-2}\right)=384}}$

$\implies{\rm{\left(4\right)^{2x}\left(\frac{1}{4}-\frac{1}{4^2}\right)=384}}$

$\implies{\rm{\left(4\right)^{2x}\left(\frac{16-4}{16\times\:4}\right)=384}}$

$\implies{\rm{\left(4\right)^{2x}\left(\frac{12}{16\times4}\right)=384}}$

$\implies{\rm{\left(4\right)^{2x}=2048}}$

$\implies{\rm{\left(2\right)^{4x}=2^{11}}}$

$\boxed{\mathbb{\pink{\rm{NOW\:COMPARE\:POWERS\:OF\:2\:WE\:HAVE}}}}$

$\implies{\rm{4x=11}}$

$\implies{\rm{x=\frac{11}{4}}}$

$\therefore$ $\rm{x=\frac{11}{4}}$