Question

For what value does (1/9)^a+1=81^a+1 12^2-a?

Answer 1

a = -4

Explanation:

`((1)/(9))^(a + 1) = 81^(a + 1) \cdot 27^(2 - a)`

`(3^(-2))^(a + 1) = (3^4)^(a + 1) \cdot (3^3)^(2 - a)`

`3^(-2a - 2) = 3^(4a + 4) \cdot 3^(6 - 3a)`

`3^(-2a - 2) = 3^(4a + 4 + 6 - 3a)`

`3^(-2a - 2) = 3^(a + 10)`

`-2a - 2 = a + 10`

`-3a = 12`

`a = -4`