Question

How do you solve `Ln (x-1) + ln (x+2) = 1`?

Answer 1

`x = 1/2 (-1 +sqrt[9 + 4 e]) = 1.72896`

Explanation:

`Ln (x-1) + ln (x+2) = 1->Ln(x-1)(x+2)=Ln e`

`(x-1)(x+2)-e=0`

Solving for `x`

`x = 1/2 (-1 pm sqrt[9 + 4 e]) = {-2.72896, 1.72896}`

Now, substituting those values in `(x-1)` and `(x+2)` keeping in mind that both must be positive, we get at the solution.

`x = 1/2 (-1 +sqrt[9 + 4 e]) = 1.72896`