Question

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

Answer 1

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

$Use:\ (a^n)^m=a^{nm}$

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

Answer: A) -8.