skylarandersen1 skylarandersen1
  • 15-11-2019
  • Mathematics
contestada

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

Respuesta :

carlosego
carlosego carlosego
  • 27-11-2019

For this case we have the following expression:

[tex]8 ^ y = 16^{ y + 2}[/tex]

We know that:

[tex]8 = 2 * 2 * 2 = 2 ^ 3\\16 = 2 * 2 * 2 * 2 = 2 ^ 4[/tex]

Rewriting the expression we have:

[tex]2^{ 3(y)} = 2^ {4 (y + 2)}\\2^{3y} = 2^{4y + 8}[/tex]

For equality to be met we have to:

[tex]3y = 4y + 8\\3y-4y = 8\\-y = 8\\y = -8[/tex]

ANswer:

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

Option A

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