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