Question

Solve for $x$ :$4^{x-1}\times (.5{)}^{3-2x}={\left(\frac{1}{8}\right)}^{-x}$

Answer 1

$4^{x-1}\times (.5{)}^{3-2x}={\left(\frac{1}{8}\right)}^{-x}$

$=>(2^2{)}^{x-1}\times (\frac{5}{10}{)}^{3-2x}=(2^3{)}^x$

$=>(2{)}^{2x-2}\times (\frac{1}{2}{)}^{3-2x}=(2{)}^{3x}$

$=>(2{)}^{2x-2}\times (2{)}^{2x-3}=(2{)}^{3x}$

$=>2^{2x-2+2x-3}=(2{)}^{3x}$

$=>2x-2+2x-3=3x$

$=>4x-3x=5$

$=>x=5$