Question

How do you solve `2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0`?

Answer 1

`x = 0 " or " x = 1/2log_5 2" or " x = 1/2log_5 (3/2)`

Explanation:

`2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0`

Take `y = 5^(2x)`

`2y^3-9y^2+13y-6 = 0`
`(y-1)(y-2)(2y-3) = 0`

`5^(2x) = 1 " or " 5^(2x) = 2" or " 5^(2x) = 3/2`
`x = 0 " or " x = 1/2log_5 2" or " x = 1/2log_5 (3/2)`