Question

What is the answer to C??

Answer 1

x = 1

Explanation:

3^2x - 9 (3^-2x) = 8

<=> 3^2x - 9/(3^2x) = 8

Given that 3^2x = y [1] (y>0), we have a new equation as follows:

y - 9×
`(1)/(y)` = 8

<=> y - 9/y = 8

<=> y(y - 9/y) = y×8

<=> y^2 - 9 = 8×y

<=> y^2 - 8y - 9 = 0

<=> (y^2 + y) - (9×y + 9) = 0

<=> y(y + 1) - 9(y + 1) = 0

<=> (y - 9)(y + 1) = 0

=> y = 9, or y = - 1

However, as 3^2x > 0, y>0.

Therefore, y = 9.

Replace y with 9 in [1], we have:

3^2x = 9 = 3^2

=> 2x = 2

=> x = 1