Question

If 8y= 16^y+2, what is the value of y?

Answer 1

y = - 8

Explanation:

Using the rule of exponents

`(a^m)^(n)` =
`a^(mn)`

Note that 8 = 2³ and 16 =
`2^(4)`

Given

`8^(y)` =
`16^(y+2)`, then

`(2^3)^(y)` =
`(2^4)^(y+2)`

`2^(3y)` =
`2^(4(y+2))`

Since the bases on both sides are equal, both 2 then equate the exponents

4(y + 2) = 3y

4y + 8 = 3y ( subtract 3y from both sides )

y + 8 = 0 ( subtract 8 from both sides )

y = - 8

Answer 2

y = -8
I hope this helps !! c: