Which equation is equivalent to 2^4x = 8^x-3?2^4x = 2^2x-32^4x = 2^2x-62^4x = 2^3x-32^4x = 2^3x-9
Accepted Solution
A:
Answer:[tex]\large\boxed{2^{4x}=2^{3x-9}}[/tex]Step-by-step explanation:[tex]8=2^3\to 8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{3(x-3)}\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=2^{(3)(x)+(3)(-3)}=2^{3x-9}[/tex]If you want a solution of this equation:[tex]2^{4x}=8^{x-3}\\\\2^{4x}=2^{3x-9}\iff4x=x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x=-3\qquad\text{divide both sides by 3}\\\\x=-1[/tex]