Question

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

Answer 1

For this case we have the following expression:

$8 ^ y = 16^{ y + 2}$

We know that:

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

Rewriting the expression we have:

$2^{ 3(y)} = 2^ {4 (y + 2)}\\2^{3y} = 2^{4y + 8}$

For equality to be met we have to:

$3y = 4y + 8\\3y-4y = 8\\-y = 8\\y = -8$

ANswer:

The value of the variable "y" is -8.

Option A