Question

Solve the following equation for x:

${\displaystyle 2^{x+1}=4^{x-3}}$

Answer 1

${\displaystyle 2^{x+1}=4^{x-3}}$

${\displaystyle \Rightarrow 2^{x+1}={\left(2^2\right)}^{x-3}}$

${\displaystyle \Rightarrow 2^{x+1}=\left(2^{2x-6}\right)}$

⇒ x + 1 = 2x - 6

⇒ 2x - x = 1 + 6

⇒ x = 7