Question

How do you solve `5^ { 2x } + 20( 5^ { x } ) - 125= 0`?

Answer 1

`x = 1`.

Explanation:

The equation can be written as

`(5^x)^2 + 20(5^x) - 125 = 0`

We now let `u = 5^x`.

`u^2 + 20u - 125 = 0`

`(u + 25)(u - 5) = 0`

`u = -25 and 5`

`5^x = -25 and 5^x = 5`

There is no solution to the first solution (because if you take the `ln` of `-25`, it is undefined). The second equation obviously has `x = 1` as a solution.

Hopefully this helps!