Question

If 8^y=16^y+2, what is the value of y?
A) -8
B) -4
C) -2
D) -1

Answer 1

-8

Explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

Answer 2

`8=2^3;\ 16=2^4`


`Use:\ (a^n)^m=a^(nm)`


`8^y=16^(y+2)\\\\(2^3)^y=(2^4)^(y+2)\\\\2^(3y)=2^(4(y+2))\iff3y=4(y+2)\\\\3y=4y+8\ \ \ |-4y\\\\-y=8\to y=-8`

Answer: A) -8.