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]
Answer: the correct option is
(D) [tex]2^{4x}=2^{3x-9}.[/tex]
Step-by-step explanation: We are given to select the correct equation that is equivalent to the following equation :
[tex]2^{4x}=8^{x-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Equivalent equations means two equations that can be obtained from one another using some properties of formula.
We will be using the following formula :
[tex](a^b)^c=a^{b\times c}.[/tex]
From equation (i), we have
[tex]2^{4x}=8^{x-3}\\\\\Rightarrow 2^{4x}=(2^3)^{x-3}\\\\\Rightarrow 2^{4x}=2^{3\times(x-3)}\\\\\Rightarrow 2^{4x}=2^{3x-9}.[/tex]
Thus, the required equivalent equation is [tex]2^{4x}=2^{3x-9}.[/tex]
Option (D) is CORRECT.
