Question

Which equation is equivalent to 2^4x = 8^x-3

Answer 1

Answer:2^4x = 8^x-3

Step-by-step explanation:Answer is D

Answer 2

x = -9

Explanation:

`8=2^3\\\\8^(x-3)=(2^3)^(x-3)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\8^(x-3)=2^(3(x-3))\qquad\text{use the distribtutive property}\ a(b+c)=ab+ac\\\\8^(x-3)=2^(3x-9)\\\\\text{Therefore}\\\\2^(4x)=8^(x-3)\Rightarrow2^(4x)=2^(3x-9)\iff4x=3x-9\qquad\text{subtract}\ 3x\ \text{from both isdes}\\\\4x-3x=3x-3x-9\\\\x=-9`